WelcometoNetica'sHelpSystemThissystemisdesignedtoofferthemostup-to-datedocumentationon=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_Application.htm');returnfalse;">NeticaApplication,theworld'smostwidelyused=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesiannetworkdevelopmentsoftware,fromNorsysSoftwareCorp.

Herearesometipsforeffectivelyfindingtheinformationyouneed:

NavigationButtons:UsethesmallwhitepreviousandnextarrowsinthesidepaneltosequentiallypagethroughtheHelpsystem.UsetheBackbuttoninyourwebbrowsertoreturntothelastpageyouwerevisitingifalinktakesyououtofsequence.

Styles:Werecommendbecomingfamiliarwiththesehyper-linkstyles,astheyareusedthroughoutthedocumentation:

=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_popup.htm');returnfalse;">popuplink=openspopuptextonyourscreen

Encyclopedialink=takesyoutoanEncyclopediapage

generallink=takesyoutoanotherpagewithinthehelpsystem

weblink=opensawebbrowserpageorenablese-mail

Glossarylink=takesyoutotheindicatedGlossaryentry

Set-up:First,opentheTableofContents(withthe"Show"orthe"Contents"button).Thenwerecommendre-sizingthewindowtoyourviewingpreference.

SequentialReading:Thishelpsystemislaidoutinlogicalchapters,

ascendingsomewhatbylevelofexpertise.Youcanreadthroughtheentiresystembyusingthesmallwhitepreviousandnextarrowsinthesidepanel(thechapterstypicallybuilduponeachother).Alternatively,youcanopentheTableofContentsandgostraighttoyourdesiredtopic.

TheIndex:WheneveryouhaveaproblemwithNetica,orneedsomeinformationonhowitisworking,yourfirststepshouldbetochecktheIndex(clicktheIndextabinthesidepanel).Wehavetakengreatcaretocreateaverycomprehensiveandusefulindex.Ifthereareentriesthatyoufeelshouldbeadded,please=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">informus.

OtherResources:ExplorehowotherpeopleareusingNeticabyvisitingouronlinelibrary.Youcandownloadnetsandmightgetsomeideasforhowbesttostructureyourcurrentnet.Wealsoencourageyoutoexploreouronlinetutorialforcomprehensiveinformationatthebeginner,intermediateandadvancedlevels.

ContactUs:Ifthereisanythingyoucan'tfigureoutbyusingthisHelpsystem,feelfreetocontactusviaemailorothermeansofcompanycommunications.

Now,itistimetoGetStarted!

GettingStartedWelcometoNeticaApplicationfrom=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsys.Neticaisaversatile,fast,user-friendlyprogramthatyoucanusetofindpatternsindata,creatediagramsencodingknowledgeorrepresentingdecisionproblems,usethesetoanswerqueriesandfindoptimaldecisions,andcreateprobabilisticexpertsystems.Itissuitableforapplicationsintheareasofdiagnosis,prediction,decisionanalysis,probabilisticmodeling,riskmanagement,expertsystembuilding,sensorfusion,reliabilityanalysis,andcertainkindsofstatisticalanalysisanddatamining.

NeticaAPI:ThisguideisforNeticaApplication;itisnotfortheNeticaProgrammer’sLibrary,alsoknownas"NeticaAPI"(ApplicationProgramInterface).TheAPIisamodulewithmuchofthesamefunctionalityasNeticaApplication,butdesignedforprogrammerstoembedintheirprograms.ForhelpwiththeAPI,usetheCAPIWebdocsorotheronlineAPImanuals.

WebSite:YoucanvisittheNorsyswebsiteforthelatestversionofNetica,versionsofNeticaforotherplatforms,NeticaAPI,examplenets,tutorialsandmoreinformation.

Version:YoucandeterminetheversionofthisguidebyclickingontheNeticaiconintheupperrighthandofthescreen.Ideally,itshouldatleastapproximatelymatchtheversionofNetica,whichyoucanfindbychoosingHelp→AboutNeticafromwithinNetica.(featuresofnewversion)

Prerequisites:ThisguideassumesthatyouarefamiliarwithusingtheMicrosoftWindowsoperatingsystem.ItalsoassumesfamiliaritywithBayesianbeliefnetworks(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnets)orinfluencediagrams,althoughitisverysuitableforsomeonewhoisintheprocessoflearningaboutthem.TolearnmoreabouttheconceptsandapplicationsofBBNs,exploreourintroductoryreferences,thetutorialnetsinourBayesnetlibrary,andthetutorialexamplesthatcamewithyour

Neticadownload.

NextSteps:Firstyoumaywanttoreadthelegalities,andadescriptionofNeticaApplicationandNeticaAPI.TheninstallNeticaandtaketheQuickTourforanintroduction.Forbackgroundreading,youmaywanttoseeintroductoryreferences.Thenyouarereadyforthein-depthtopicsofNetica.

Feedback:Please=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">emailNorsyswithyourquestionsandcommentsaboutNeticaorthisonscreenhelpdocument.Tolearnmoreaboutourdesignphilosophy,clickhere.

NeticaApplicationNeticaApplicationisacomprehensivetoolforworkingwithBayesian=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">beliefnetsand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets(influencediagrams).Itcanbuild,learn,modify,transformandstorenets,aswellasanswerqueriesorfindoptimalsolutionsusingitspowerfulinferenceengine.Thisversionhasmanynewfeaturesandmanymorearecurrentlyunderdevelopment.

NeticacanalsoworkonaMac.MoreInfo

Clickherefornewfeatures.

Features:•CompilesBayesnetsintojunctiontreesofcliquesforfastprobabilisticreasoning.

•Canlearnprobabilisticrelationsfromdata(includingEMandgradientdescentlearning).

•Generatespresentationqualitygraphicswhichcanbetransferredtootherdocuments,includingSVGgraphics.

•Allowstheentryofprobabilisticrelationsbyequation,withanextensivebuilt-inlibraryofprobabilisticfunctionsandothermathematicalfunctions.Theequationscanbedeterministicorprobabilistic,andfordiscreteorcontinuousvariables.

•ProvideseasygraphicaleditingofBayesnetsandinfluencediagrams,including:•Cuttingandpastingofnodesandnetswithoutlosingtheirprobabilisticrelations.

•Manywaysofdisplayingnodes(bargraphs,meters,etc.)•Linkswithbendstokeepcomplexdiagramsorderly.•Allowsenteringcommentstodocumenteachnode,keepstrackofauthor,

whenchanged,etc.•Unlimitedlevelsofundo/redo.•Cancreateandworkwithsetsofnodesincludingcolor-codingnodes.•Commentwindowsfornodes,linksandstates.•Dynamicscrollingandmousewheelsupportedeverywhere.

•Canfindoptimaldecisionsforsequentialdecisionproblems(i.e.laterdecisionsaredependentontheresultsofearlierones).

•CantesttheperformanceofaBayesnetusingafileofcases.Neticawillprintoutaconfusionmatrix,errorrate,logarithmicandquadratic(Brier)scoringruleresults,calibrationtableandsurpriseindexesforeachnodedesired.

•Candoutility-freesensitivityanalysis.•Canreverseindividuallinksand“sumout”nodesofinfluencediagramsorbeliefnets,formodelexplorationandrefinement.

•Supportsdisconnectedlinks,whichmakespossiblelibrariesofprobabilisticrelationships.

•Hasfacilitiestoenterandupdateindividualcases,storethemintheirownfiles,andapplythemtootherBayesnets.

•Hasfacilitiesfortheeasydiscretizationofcontinuousvariables.•Hasnobuilt-inlimitsonthesizeorcomplexityofnets,sotheyarelimitedonlybyavailablememory.

•Canworkhand-in-handwiththe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPIProgrammer’sLibrary.

•CandirectlyconnectwithadatabaseorExcelspreadsheetforlearning,readingcases,testinganet,etc.

•Hasbinary.netaformatforfasterandsmallerfiles(text-based.dnefilesstillhavecompletesupport).

•Canobfuscatenets,andcanworkwithencryptedBayesnets,toprotectyourintellectualproperty.

•Canautomaticallyreadinacase,compiletheBayesnetwhenitisreadfromdisk,andhasauto-discretization,basedoncasefiles.

FAQs-RunningNeticaonaMacTogetNeticatoworkonyourMac,you’llneedtofirstinstallacompatibilitylayerforrunningWindowsprograms,andthenyoucaninstallNeticaintheusualway.Thereareseveralpossibilitiesforcompatibilitylayers(seebelow),butwehavefoundthatCrossOverisoneoftheleastexpensiveandeasiest-to-useoptions.ItallowsNeticatorunwithfullspeedandcapability.Neticahasbeencreatedtorunwellundereventhemostbasicofconditions,sotherearenoseriousissuesusingNeticaunderCrossover(checkouttheirreviewofNetica’scompatibility).Seethebottomofthisscreenfortheknownissuesandsimplework-aroundsforrunningNeticaonyourMac.WhyamIdownloadingatrialversionofCrossOver?Codeweaversoffersa30dayfullfeaturedversionofCrossOver,soyoucantryitoutforfreeandgetsupportalongtheway.Onceyou’resatisfiedwithitsperformanceonyourMac,youcanpurchaseitfor$39.95(whichgoestosupporttheopen-sourcedevelopment).AretherealternativeoptionstousingCrossOver?ThereareotheroptionsforrunningWindows-basedprogramsonyourMac,suchasParallels,VMwareFusion,andAppleBootcamp.Eachsolutionhasitsadvantagesanddisadvantages.Neticaworkswellonallofthem.TheseothersolutionswillenableyoutorunawidervarietyofWindowsprogramsbutaremoreexpensiveandlarger.Thisdifferentiationchartmaybehelpfulinmakingyourdecisionandtherearemanyotherreviewsonline.IsthereawaytogetWINEonmymachineforfree?IfyouarecomfortablewithamoretechnicalapproachtogettingWINEonyourmachine,youcantryoutthefreeWineBinaryDownloads,aswellastheRecommendedPackagesforbuildingWineon32bit.WillthisdownloadpollutemyMac?

No!CrossOverisjustacompatibilitylayer(inotherwords,youarenotactuallyinstallingWindowsonyourMac),anditwon’taffectanythingelseonyourMac.CanIeasilygetridofCrossOverifIdecideIdon’twantitonmymachine?Yes!ToerasealltracesofCrossOver,followthesesteps.I’mhavingtroubleinstallingCrossOver,help!GothroughthestepsoftheofficialInstallationGuide.Ifyou’restillhavingtrouble,checkouttheirFAQpage.OnceIgetNeticarunningonmymachine,arethereanyknownproblemswiththesoftware?Thereareafewminorissues,allwithquickwork-arounds:1.Right-clicking:Control-click,asyou'reprobablyusedtowithMacprograms,doesn’tworkthatwayunderWINE(sofar).

Workaround:Enablesecondaryclick.Todothis,gotoSystemPreferences>Keyboard&Mouse>Trackpadandenable‘Taptrackpadusingtwofingersforsecondaryclick’.Youcanthenright-clickbytappingthetrackpadwithtwofingers.Update:IfyouarerunningacurrentversionofXquartz,youcangointotheX11.apppreferenceswhenit’srunningandselectwhatyouwanttobemodifierkeysforrightandmiddleclicks.

2.Messageswindow:WhenNeticafirstopens,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowappearsinwordformatintheupperleftofthescreeninsteadofbottomleft.

Solution:Double-clickthewordtoopenthewindow.Movingforward,theMessageswindowmayappearasablankwhitesquareinthebottom

leftoftheNeticascreen.Again,youcandouble-clickthewhitesquaretobringuptheMessageswindow.

3.OnscreenHelp:thehelpsystembuiltintoNeticadoesnotlaunchwhenclicked.

Solution:UsethisonlineHelpsystemforassistanceandfordocumentationonallthelatestfeatures.

4.LearningfromExcelfiles:YouwillgeterrormessagesifattemptingtolearnfromanExcelfile.

Solution:YoumustconvertyourExcelcasefileintoatextfileandthenyoucanproceedwiththestepslistedinLearningFromaCaseFile.

HelpusimproveNetica'sfunctionalityonMacbysendingusyourquestionsorfeedback!

NewFeaturesTocheckyourversionofNetica,openNeticaandchooseHelp→AboutNetica.Dependingonyourversion,youmaywanttocheckforrecentpre-releaseversions,availablefromourftpsite.

YoucantryanyversionofNeticain'limitedmode'(withoutapassword).Or,youcanupgradeyourcurrentNeticalicense.

Inadditiontoitsstandardfeatures,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_Application.htm');returnfalse;">Neticahasthefollowingnewfeatures.

Version4(-)andversion5(•)newfeatures:

•GeneratewebsitesfromBayesnets:AftercreatinganyBayesnet,youcanselectthetargetnodes,pushabuttonandyourbrowserwillspringuprunningyourBayesnetasaquestion/answersystemorasadashboardwithsliders.Bestofall,yourwebsiteisalreadydeployedtotheworldhostedonoursystem(oryoucanhostit,ormakeadesktop-onlyversion).SeeExamplesite.

Fullusageofthissystemissoldasaseparateproduct,andcompletedocumentationforthisfeatureisinaseparatemanual.ContactNorsysfordetails.

•StructureLearning-NeticacannowdoTANlearningoflinkstructurefromdata.Overtheseriesofversion5releases,wewillbefurtheraddingtoNetica'slearning-from-datacapability(structure,parameter,testing).

-CustomReports-CangeneratehighlycustomizablereportsonmanyaspectsoftheBayesnet,nodes,states,CPTs,cases,findings,beliefs,sensitivityresults,otherinferenceresults,etc.Thereportscanrangefrombasictextoutputtonicelyformattedtables.TheycanbeintheformofHTML,XML,text,richtext,etc,basedontemplatefilesthatyoumakeorchoosefromourlibraryoftemplates.

•Actions-Canenteractionsorinterventions(i.e.,Pearl'sdo-calculus)tonaturenodesinsteadofjustfindings.Alsohandlescalibrationactions(aka

randomizedactionsorpopulationinterventions).•Candirectlymovebeliefbarswiththemousetoentercalibrationfindingsandcalibrationactions

•MajorimprovementstodynamicBayesnet(DBN)capabilityfortimeseries.Nowdoesa"burn-in"togenerateinitial-statenodes.

•EMlearningnowhandlesmultipleCPTtablesconstrainedtobethesame(indicatedbytheuserfield"CPT_ID"havingthesamevalue).

-BuildtablefromothernetisaveryversatilefeaturethatamongotherthingscanfilltheCPTtablesofnodesinonenetbasedonanothernetwithadifferentstructure.

-Optionforinferencebysamplingwhennecessary(usingrejectionmethod).•CannowdoallBayesnetoperations(suchasinference)whentherearesomedisconnectedlinks.

-Capability"SplitNode"convertsamulti-statenodeintoasetofBooleannodes,onenodeforeachstateoftheoriginalnode.

-Cansortthestatesofanode(ornodes)byname,belief,othernode,standardorder,reverseorder.Standardorderisuser-definable.Othernodeisveryinteresting;itusesBayesianinferencetomaketheordercompatiblewiththeorderingofstatesofanothernode(theselectednode).

-AddedNoisyOrMultiDistfunction,availablefromequations,togeneralizethenoisy-ortomultiplestates,inawayusuallymorefittingthannoisy-maxdoes.

-Adding/Deleting/Renamingstatesbyright-clickingcannowdomanystatesatatime(eventomultiplenodes),andcanaddstatenames,numbersandtitles.

•InNode-setdialog,shift-clickingtheSetColorbuttonwillauto-colorallnode-setsfromthefirstonetotheselectedone,inclusive.

•EMlearningnowleavesfindingsinnetwhileoperating(andhandlesthemproperly;theycanoverridethecasefile).

•Cannowhavepasswordsthatworkforallusersonamachineoracrossanetwork.

•Fixed:PasswordswouldnotstayregisteredonsomeAsianMSWindowsmachines.

•GreatlyimprovedtheCombineNetsfeature.•AddedtotheModify→OrderStatesoptions.•Onscreenhelpnowalsohasanonlineinternethelpsystem,anditisavailablefromNetica'smenu.

Othersmallerimprovements

Fromversion3.16toversion3.25:

•Youcanchangetheorderofparentswhileeditinganode'sCPTtable(andtherebythestructureofthetable)justbydraggingitscolumns.

•Thereisnowagreatnewwaytonavigatelargenetdiagrams,calledGlobalZoom.Alsonewis"pushscrolling",donebyholdingtheALTkeydownanddraggingonthebackground.

•Providestheabilitytodothesameoperationtomanynodesatonce,suchas:adding,removing,renamingorreorderingstates,changingdiscretizationthresholds,enteringfindings,enteringuser-definedfields,etc.

•Whenyouchangethenameofnode,itautomaticallyadjuststhatnode'sequationandtheequationsofitschildnodes.Alsoworksfornamechangesduetoduplicatingnodesandtimeexpansions.

•Addedmuchwidersupportforright-clickingonnodes,net,link,etc.•Canviewandedittablesofanode's'experience'andfrequencycountswhenlearningfromdataorconnectedtoadatabase.

•Improvedauto-discretizingalgorithm.•Added“CombineNets”feature(inpreliminarystage).Othersmallerimprovements

Fromversion2.17toversion3.16:

•Cancreateandworkwithsetsofnodes.•Cancolor-codenodes.•CandirectlyconnectwithadatabaseorExcelspreadsheetforlearning,readingcases,testinganet,etc.•CangenerateSVGgraphicsofBayesnets,forqualityweborprintpublishing.

•Hasanewbinary.netaformatforfasterandsmallerBayesnetfiles(text-based.dnefileswillalwayscontinuetohavecompletesupport).•Canobfuscatenets,andcanworkwithencryptedBayesnets,toprotectyourintellectualproperty.•Hasauto-discretization,basedoncasefiles.•Whenhovercursorovernodes,statesorlinksNeticacandisplayacommentofyourchoiceinafloatingwindow.•Casefilescannowhaveuncertainfindingsusingaverysimplebutpowerfulfileformat(UVF),andthoseuncertainfindingswillbeproperlyhandledbyNetica'sbeliefupdating,EMlearning,processcases,etc.•AutomaticallycompilestheBayesnetwhenitisreadfromdisk,whenappropriate.•TheMeterdisplayfordiscretizednodes,orthosewithstatevaluesdefined,nowhasaneedlewhichshowsexpectedvalue,andabandarounditwhichdisplaysstandarddeviation.•Keepstrackofwhentablesmayneedtobere-builtfromtheirequations.•ManyimprovementstotheCPTtableeditor,includingbetterpasting,betterscrolling,applyinganoperationtomultiplecells,probabilitiesorpercentages,experience,etc.•Dynamicscrollingandmousewheelsupportedeverywhere.•NowhasaCalibrationchoiceonenter-findingsmenu,toenterthelikelihoodfindingthatwillresultinacertainbeliefstate.•Fixedbugs,including:•Whencopy/pastingnetgraphics,onsomesystems,thelowerrightoftheimagewascutoff.•Inthenodepropertiesdialog,repeatederrormessagessometimesmadeitdifficulttoexit.•BelieflinkingtomodernversionsofExceldidn'tupdatelinks.•Printingdidn'tworktosomenetworkprintersorthosewithlongnames.•NowalsoreadsHugin6.*.netfiles(aswellas4.*and5.*).•AddedTable→EnterExperiencecommandtoenterexperiencetablesforallselectednodesatonce.•Thereisnowa"-case"commandlineparametertoautomaticallyread-ina

case.•Theexpectedvalueofanodeisdisplayedevenifoneoftheintervalsextendstoinfinity.

Fromversion1.12toversion2.17:

•HasEMlearningandgradientdescentlearningofCPTtablestobetterdealwith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdata.•HasaProcessCasesfeature,toreadcasesfromafile,processthemwiththeBayesnetone-by-one,thenoutputtheresultstoanewfile.•NowhasaRecentFileslistonthemenu.•Added“GoBack”keycommandtoscrolltothelastplacebeingeditedonanet.•CannowcompileandupdatenetswhoseCPTsorutilitytablesareabsentorincomplete(takesmissingentriesasuniformprobabilitiesorzeroutilities).•Thereisanodepalettewindowtokeepcommonlyusednodes.•Generatingatablefromanequationcanusetheintegraloftheequation,insteadofsampling,formanycommondistributions.•Auto-updatingnowworkswheneveritcan(e.g.,afterchangingaCPT).•Cansimultaneouslyaddlinkstomanynodes,orfrommanynodes,iftheyareselectedwhenaddingalink.•Improvedtimeexpansion,cannoweditdelaysinnodedialog,andthereisaModify→DelayLinksmenucommand.•CannowreadDXpressfilesandBNIF(.dsc)files.•AddedNoisy-MaxandNoisy-Sumcapabilities(Noisy-OrandNoisy-Andalreadyexist).•Cannowobserveandsetnodeuserfieldsusingthenodepropertiesbox.•Windowtitlehasindicator(*)toshowwhenithasunsavedchanges•Displays*deterministic*naturenodesinLabelBoxstyleusingathickborder.•CommandlinecanacceptaNeticapassword(-passwordxxx),whichisused

forthatsession,butnotenteredintotheregistry.•Inferencealgorithmtakesbetteradvantageoffindingsenteredtospeedinference.•Equation-to-tableexpandstheintervalautomaticallyifvaluesareout-of-bounds.•Addedlogmessagescommand.•CansetthedisplayofnodestatestoonlytheNmostprobable,orderedbymostprobablefirst,whichchangesasbeliefschange.•Whenenterfindings,andbeliefupdatingnotyetdone,onlythosenodesaffectedwillhavetheirbeliefsindicatedinvalid.•Whenpastenodesintoanetworkitexpandsthedrawingsizeifnecessary(insteadofcrunchingthemup).•AddedaSelectNodesmenuwhichcanselectnodeswithequations,findings,dependenton,parents,ancestors,childrenanddescendentsofselectednodes.•AddedaSelectLinksmenuwhichcanselectlinks:all,disconnected,ineffectual(zerostrength),formingcycle,orentering,exitingorinterconnectingselectednodes.•=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_updating.htm');returnfalse;">Deterministicupdatingprecedesbeliefupdating,foraccuracyandspeed.•Canreadorcreatecasefileswithcomma,spaceortabdelimiters,andwith?,*,spaceornothingas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdatachars.•Casefilesdon'tnormallyhaveaheaderwith//~->[CASE-1]->~andatime/authorstampanymore(althoughstillacceptsthat).•AddedLayout→SpreadOut/Compactcapability.

InstallationLegal:BeforeinstallingorusingNetica,besurethatyouaccepttheLicenseAgreementwhichisalsoprovidedwiththesoftwareinaseparatedocument.

Requirements:NeticaApplicationrequiresaPCrunninganyversionofMicrosoftWindowsfrom2000toWindows7(includingXPandVista).IfyouneedaversionofNeticaforanearlierversionofWindows(suchasWindows95),then=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">contactNorsys.Installationrequireslessthan10MBofharddiskspace.(ReasonforNetica’ssmallsize)

NeticawillrunwellevenonaveryslowPC(0.4GHz),usingverylittleRAM(about30MB),butworkingwithcomplexBayesnetsmayrequiremuchmorespeedandlargeamountsofRAM.

Install:1.FirstobtaintheNeticapackagefile.YoumayobtainitbydownloadingfromtheNorsyswebsite,orotherwisefromNorsys.ThenameofthefilewillbeNetica_Win.exe.2.Choose“Run”fromthedownloaddialogbox,orsavethefiletodiskandthendouble-clickitsicon.3.Whenadialogboxappears,enterwhereonyourharddiskyouwanttheNeticafolderplaced.Youcanputitanywhereyouwish;popularchoicesareC:\NeticaorC:\ProgramFiles\Netica.Makesurethereisadriveletter(e.g.“C:\”)atthefrontofthelocation.Youdon’thavetoincludeversioninformationinthename,becauseafoldercalledNetica###willbecreatedwithinit,where###istheversionnumber.4.ClicktheUnZipbuttonandthenclosethedialogbox.

MacInstallation:ToinstallNeticaonaMac,followthesesteps.Onceyou'vecompletedinstallation,you'llwanttobecomefamiliarwiththeFAQforrunningNeticaonyourMac.

Running:Then,opentheNetica###folderfromwhereyouhaditplaced.Thisfolderisknownasthe=4&&typeof(BSPSPopupOnMouseOver)==

'function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_Glossary_FM.htm#homedirectory');returnfalse;">homefolder.WithinitwillbeallthefilesrequiredforNetica,includingtheexecutablefilecalledNetica(orNetica.exe),withthis icon.Thefirsttimeyourunityoushouldright-clickonit,andchoose"Runasadministrator"(ifyouwantyoucanrunitbyjustdouble-clickingit,butthenitmightnotbefullyregisteredwiththesystem).Onsomesystemsitmaytakealongtimetostartthefirsttime;pleasebepatientandknowthatnexttimeitwillstartlightening-fast.

Password:Theenter-passworddialogboxwillappear,soifyouobtainedalicensepasswordfromNorsysbye-mailoronyourinvoice,youmaytypeitin,orbetteryetcopyandpasteitin.Ifyoulaterwishtoremoveorchangethepassword,chooseFile→NeticaPasswordfromNetica’smenu.

LimitedMode:YoucanuseNeticawithoutapassword(i.e.'LimitedMode'),anditwilloperateinafullfeaturedandusefulmanner,butwillnotbeabletodolargerprojects(i.e.can’tsavenetswithmorethan15nodes,learnfrommorethan1000casesatatime,etc.)

Next:NowthatNeticaisinstalledandrunning,youcangetanintroductiontohowitworksbydoingtheoperationsdescribedintheQuickTour,orcheckouttheNewFeatures.

IfyouwishNeticatobeonyourStartmenu,youcanusethenormalWindowsmethodofdraggingtheNetica.exeicon fromtheNetica###folder(asmentionedabove)anddroppingitontheStartbutton.Ordragittothedesktopifyouwanttomakeashortcutthere.

YoucanmovetheNeticafoldertowhereveryouwantonyourharddriveatanytime.Aftermovingit,youwillagainneedtorunNeticaasAdministratoronce(asdescribedabove)toregisterthenewlocation.

MultipleVersions:IfyouhaveseveraldifferentversionsofNeticaonyourharddiskatthesametime,oneofthemwillbethe"default"(e.g.itwillbetheonethatwillrunwhenyoudouble-clickaNeticadocument).Tochangethedefault,simplymanuallyrunoncetheversionofNeticaasAdministrator(asdescribedabove).ThereisneveranyneedtouninstallanyNeticaversionbeforeinstallinganynewone.

Uninstall:TouninstallNetica,justdeletethe“Netica”folder.Neticadoesnot

addanyotherfilesanywhereinyoursystem(exceptofcourse.neta,.dneor.casdocumentsthatyoucreategetplacedwhereyousavethem),andNeticaaddsverylittletotheWindowsRegistry.IfyouhaveseveralversionsofNetica,youcanuninstalloneversionbysimplydeletingitsfolder;thatwon’tdeleteanyfilesneededbyanyotherversion.

MenuItemsandtheToolbarInthisguide,Netica'smenuitemsareindicatedinbold,witharrowsindicatingchoicesorsubmenus,soFile→Openmeanschoose“Open”fromthe“File”menuofthemainmenubar.Mostmenuitemshaveacorrespondingtoolbarbutton,andfromwithinNeticayoucandiscoverwhatthebuttonsdobyrestingthecursoronthembriefly.Forexample,itwillsay“OpenFile”,whenyourestitonthe toolbarbutton.

SomeofthetoolbarbuttonsdiscussedinthisguidemaynotappearonthetoolbarwhenyoufirststartNetica,soyoumaywanttocustomizethetoolbar.

Insteadofusingthemenuoratoolbarbutton,youcanoftenuseakeyboardshortcutoraright-clickmenu,whichhaveafewadditionalfeaturesnotavailablefromtheoverheadmenu.

QuickTourThisquicktourwillguideyouthroughsomeofthemajorfeaturesofNetica.AllyouneedtoknowtocompletethistourishowtouseMicrosoftWindows.Youdonotneedknowledgeof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnets,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetsor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica.htm');returnfalse;">Netica,althoughyoumaynotfullyunderstandwhatishappeninguntilyouhavethatknowledge.

First,makesureyouhavecompletedtheinstallation.Youshouldduplicatethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolderincaseyouaccidentallychangesomeofthesuppliedfiles.Next,runNeticabydouble-clickingonitsicon .ThefirsttimeyourunNeticaitwillaskyouforapassword.Enterthelicensepasswordsuppliedtoyouby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsys,orclickonthe“LimitedMode”buttonifyoudon’thaveone.

TheworkspacewindowwillopenandinitslowerleftcornertherewillbeaniconforaminimizedwindowcalledNeticaMessages.Clickonthe buttontoopenitup,orchooseWindow→Messages.Inthiswindow,Neticawilloftenputusefulmessageswhileitisoperatingandsometimesitwillbeeptoalertyoutoanewmessage.

Tip:Itisagoodideatoleavethe=4&&

typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">MessageswindowopenwhileyouarelearningNetica.Youcancopyandpasteinformationbetweenthiswindowandanytextfile,whichmaybeusefulforfuturereference.Itmayalsohelpbyexplainingwhysomeunexpectedoutcomehasoccurred.

GettingHelp:IfyouhavequestionsatanytimewhileusingNeticayoucangethelpbychoosingHelp→ContextHelporpressingF1.Dependingonwhatyouareworkingon,NeticawillbringupaHelppageofcommonsubjectsorwilltakeyoudirectlytoarelevantscreenwithinthehelpsystem.Ifyouwantmoreinformationonacertaintermyoucanaccessthecomprehensiveindexdirectly,bychoosingHelp→Help.Ifyouareconnectedtotheinternet,youcanfindotherkindsofhelpfromtheHelpmenu,suchas:NorsysWebsite,OnlineNeticaWebHelp(thewebversionofonscreenhelp),NetLibraryWebsite(ourlargecollectionofexamplesnets),orEmailNorsys(tosendanemailtooursupportteam).

WhenyouarefinishedwithyourNeticasession,youcanenditbychoosingFile→Exitfromthemenu.Ifyouhavecreatedorchangedsomeworkwithoutsavingit,Neticawillaskifyouwanttosaveitbeforeterminating.

Toproceedthroughthestepsofthetour,usethenavigationarrowsabove.

Activities–PARTOFQUICKTOUR

Onceyouclickonanactivitybelow,proceedthroughitspageswiththenavigationarrowabove.Eachoftheactivitiesofthequicktourmayrequireknowledgeofapreviousactivity.

1ProbabilisticInference2NetConstruction3NetTransformation4LearningfromData5Decision-MakingNets6EquationsandTimeExpansions

ProbabilisticInference–PARTOFQUICKTOUR

Tutorial:Tobegin,wewillreada=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetstoredondisk.ChooseFile→Openfromthemenu,andwhenthestandardfile-openingdialogboxappears,useittoopenthefilecalled“ChestClinic”inthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder.AwindowwillappearcontainingaBayesnetconsistingofseveralconnected=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodes.ThisverysimplenetfordiagnosingpatientsarrivingataclinicisaclassicexampleoftenusedtointroduceBayesnets.

Youcanpreparethenetfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">inferencebychoosingNetwork→Compilefromthemenu,orbyclickingthe toolbarbutton(iftheyaregray,thenethasalreadybeencompiled).Whenthecompilationiscomplete,thedefaultdisplaystylechangessothatnodesaredisplayedwithbargraphsshowingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsforeachoftheirstates.Youcanentera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">finding(alsoknownasan“observation”,or“evidence”)foranodebyclickingonthenameofthefindingtotheleftofthebargraph.Youcanalsoenterafindingby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthenodeandchoosingEnterFinding.

Whenthefindingisentered,thedisplaysofallthenodeswillbeadjustedtoaccountforit.Forinstance,puttingan‘abnormal’findingforthe‘XRayResult’nodeincreasesthebeliefthatthepatienthaslungcancerfrom5.5%to48.9%,butthenindicatingthatthepatienthasmadeavisittoAsiadecreasesthatbeliefto37.1%,becausetheabnormalXRayispartially=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_explaining_away.htm');returnfalse;">explainedawaybyagreaterchanceofTuberculosis(whichthepatientcouldcatchinAsia).

Ifyouchoose“Unknown”fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_findings_menu.htm');returnfalse;">findingsmenu,thenanyfindingforthatnodewillberetracted,andifyouchoose“Likelihood”youwillbequeriedfortheprobabilitiesofan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">uncertainfinding(“virtualevidence”)forthenode.Youcanalsoclickdirectlyonthenameofthefindingasecondtimetoretractthefinding.

Eachtimeyou=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteror=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">retractafinding,thebeliefsofallthenodeswillimmediatelybe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">updatedtoaccountforthenewinformation.IfyouwishupdatingtoonlyoccurwhenyoudoaNetwork→Updatecommand,youcanturnofftheauto-updatefeatureby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggling

Network→AutomaticUpdating.

Ifyouwanttoobserveorchangethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobabilitiesofanode(whichexpressits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationwithits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentnodes),=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodebyclickingonceonit,andthenchooseTable→View/Edit,orclickonthetoolbarbuttonwiththe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_relation_symbol.htm');returnfalse;">relationsymbol: .Aspecialwindowcalledthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogboxwillopenwhichdisplaystheprobabilitiesinatable.Theleft-handsideofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_contingency_table.htm');returnfalse;">tablecontainsaverticallistofparentconfigurations,andforeachconfigurationtheright-handsidehasafewprobabilities,expressedaspercentages.

Eachcolumnoftheright-handsidecorrespondstoadifferent=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">stateofthenode.Soeachnumberrepresentstheconditionalprobabilitythatthenodetakesonthestateindicatedbythecolumnthenumberisin,giventhattheparentshavetheconfigurationindicatedbytherowthenumberisin.Ifthenodeis=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministic(e.g.the“TbOrCa”node),thenthetabledialogboxwilldisplaya=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontable.Thisisthesameastheconditionalprobabilitytable,exceptthattheright-handsidesimplyhasthestateofthenodewhichisthefunctionvalueforthatparentconfiguration.

ToworkwithexamplesofmorecomplexBayesnets,openthefilecalled“Alarm”(alsointhemedicaldomain),orthefilecalled“HailFinder”(weatherprediction).YoucancompilethemanddoinferenceinthesamewayasyoudidwithChestClinic.Withthisexample,youcanclickdirectlyonthenameofthefindingasecondtimetoretractthefindingorholddowntheSHIFTkeywhileclickingonthenameofthefindingtoentera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativefinding.

Ifyouhaveenteredanumberoffindingsforaparticular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">caseandwishtosavethemintheirownfile,chooseCases→SaveCaseAsandenterthefilenameinthedialogboxwhichappears.IfyouwanttoworkonanewcasechooseCases→RemoveFindings,andthenenterthenewfindings.Torecovertheoriginalcase,chooseCases→GetCaseandpickitsnamefromthedialogboxwhichappears.

Whenyouaredonewithanetwindow,youcangetridofitbyclickingthebuttoninitstitlebar,orbymakingitthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activewindowandthenchoosingFile→Close.

NetConstruction–PARTOFQUICKTOUR

AddingNodes:ChooseFile→New→Networkfromthemenutocreateanew=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">beliefor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetwindow.Toadda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenode(i.e.a“chancenode”or“deterministicnode”),movethecursortothetoolbarandclickthe toolbutton.Whenyoureturnthecursortothenewwindow,itwillchangetoanellipse,andwhenyouclickinthewindow,anodewillbeaddedatthecursor.Thenodewillbeselectedwhenfirstadded(i.e.displayedwithnegativecolors),soifyoujustpresstheENTERkey,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogboxwillappearwhichallowsyoutoenterthename,states,etc.ofthenode.

=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">Utilitynodes(alsoknownas“valuenodes”)or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodesmaybeaddedinthesamewayasnaturenodes,byusingthe ortoolbuttonsrespectively.MoreInfo

AddingLinks:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">Linksmaybeaddedbyclickingthe toolbutton,thenclickingonthenodeyouwantthelinktocomefrom(i.e.the“=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parent”node),andfinallyclickingonthenodeyouwantittogoto(i.e.the“=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">child”node).Alternately,youcanclickdownintheparentnode,andwhileholdingthemousebuttondown,dragthecursortothechildnode,andthenreleaseit.Ifyoudouble-clickonatoolbarbuttonthenitwillcreateacursorthatyoucanusetoaddseveralnodesorlinks(withoutitswitchingbacktothepointereachtime).

Anotherwaytoaddnodesorlinksisto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchooseModify→NewNodeorright-clickonanodeandchooseLinks.MoreInfo

SelectingNodes&Links:To=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectanodeorlink,clickonceonitwiththeregularpointercursor,anditwillbecomehilited.Agroupofnodesmaybeselectedbyclickingdownonthebackgroundwithinthewindow,andthenmovingthemousewiththebuttondepressed(i.e.“dragging”),sothattheselectionrectangleisoverthem.YoucanaddtoorremovefromagroupofselectednodesbyholdingdowntheCTRLkeywhileyouselectthenewnodes.Todeletenodesorlinks,selectthemandthenpresstheDELETEkey.MoreInfo

UndoingOperations:Afterdoinganyoperation,youcanundoitwithEdit→Undo(orpressingCTRL+Z).Byrepeatingthisyoucanundooperationsprevioustothatone(atleast4operations,andsometimesmoreiftheydon'ttakemuchmemory).Afterundoingoneormoreoperationsyoucanredothemone-by-onewithEdit→Redo(orpressingCTRL+SHIFT+Z).WhenexploringwithNetica,itisveryusefultobeabletotryafewoperations,andtheneasily

undothem.MoreInfo

MovingNodes:Anodecanbemovedbyclickingdownonit,draggingittoitsnewposition,andthenreleasingthemousebutton.Tomoveagroupofnodes,firstselectthem,andthenclickdownononeoftheselectednodesanddragittoitsnewposition.Tochangetheshapeofalink,firstselectitbyclickingonit,thenclickdownonitagainanddragthecursortothepointwhereyouwantthelinkbendtobe.MoreInfo

Disconnecting&ReconnectingLinks:Alinkcanbedisconnectedbyclickingonittoselectit,thenclickingdownonthehilitedsquarethatformsatitsnon-arrowend,anddraggingitawayfromtheparentnode(orbyselectingthelinkandchoosingModify→DisconnectLinks).Toreconnectthelinktoanewnode,dragthenon-arrowendoverthenewparentandreleasethemousebutton,orchooseModify→ReconnectLinks.Disconnection/reconnectionisusefultochangethelinksofanetwithoutlosingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">conditionalprobabilitytablesofthenodes.RememberthattojustdeletealinkyousimplyselectitandthenpresstheDELETEkey.NOTE:Ifyoudeletealinkandthenre-addit,youwillhavelosttheinformationinthepreviousCPT;thusifyouwanttoretaintheCPTs,usethedisconnectioncommand.MoreInfo

Cutting&PastingNodes:Youcancutandpastenodesandsubnetswithinawindow,orbetweenwindows.TryopeninganetsuchasCar_Diagnosis_0,selectpartofit,pressCTRL+C(tocopyittothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboard),CTRL+N(tocreateanewnet),clickinthemiddleofthenewwindow(toindicatewheretoputit),andthenCTRL+V(topasteitintothenewnet).Youcancutandpasteotherpartsofthenet(orothernets),addnodes,etc.andthenconnectupthedisconnectedlinksasdescribedinthepreviousparagraph.Inthiswayyoucantakeknowledgefrompreviousapplications,perhapssaveitinanetfragmentlibrary,andre-useittoconstructanewnetforanewapplication.MoreInfo

SavingNets:AtanypointyoucanchooseFile→Savefromthemenutosavethecurrentversionofthenettofile,overwritingthepreviousone,orFile

→SaveAstosaveittoanewfile.

NodeProperties:Youcanchangethepropertiesofanodebyusinganodedialogbox,whichisobtainedbydouble-clickingonthenode,(orbyright-clickingandchoosingProperties).Whenyoumakechangesinthedialogbox,theywon’tactuallybeappliedtothenodeuntilyouclickthe“Apply”or“Okay”buttons.Youcanchangeanode’snameortitleintheobviouswaybytypingintheappropriatetextfieldofthedialogbox.Tochangethenameofoneofthenode’sstates,choosethestateusingthedown-arrowbesidethe“State:”label,andthentypeintheneighboringtextfield.Youcanaddordeletestateswiththe“New”and“Delete”buttons.Mostpeoplefinditmoreconvenienttoenterorchangestatenamesusingthetextentryareaatthebottomofthedialogbox.NOTE:Ifyouaddordeleteastatefromthenodedialogbox,youwilllosetheinformationinstatecommentsandintheCPT.Instead,addordeleteastateusingtheright-clickmenu.MoreInfo

Thetextentryareaatthebottomofthedialogboxcanbeusedtoenterorchangeseveraldifferentthings;youchoosethethingtoworkonwiththeselectordirectlyaboveit.Forinstance,toentersometextdocumentingthenode,youchoose“Description”withtheselector,andthentypeinthetextentrybox.Somechoices(suchas“WhenChanged”)can’tbemodified;theyareforviewingonly.MoreInfo

NodeCPTs:Inordertochangetheprobabilitiesofanodeconditionedonthevaluesofitsparents(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTs),firstopenthenode’stabledialogboxby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingit,andthenchoosingTable→View/Edit.Youcanclickonanumber(orstatenameifit’sadeterministicnode)tochangeit.Ifnoprobabilitieshaveyetbeenenteredforthisnode,youcanclickonanemptycelltoenteranumber.Thenumbersmustbeenteredaspercentages.Youcanselectsomecellsbyclickingdowninacellthatisnotcurrentlybeingedited,anddraggingtoenclosethecellsbeforereleasingthemousebutton.Youcanselectwholerowsatatimebyclickinganddraggingslightlytotherightofthedoubleverticalline(thisishowyoumustselectdeterministiccells,sinceclickingdirectlyonthembringsupthestatemenu).Thereareseveralitemsinthe

Tablemenuthatyoucanusetosetthevaluesofselectedcells(suchasUniformProbabilities,FillMissing,NormalizeandRandomize).AnychangesyoumakeinthedialogboxwillnotactuallybetransferredtothenodeuntilyoupresstheApplyorOkaybutton.Thesetwobuttonsdothesamething,buttheOkaybuttonalsoremovesthedialogbox.MoreInfo

NodeStyles:Tochangethedisplaystyleofsomenodes,firstselectthemandthenmakeachoicefromtheStylemenu.FortheChestClinicnetthemostusefuldisplaysareBelief-barorMeter,althoughifyouwerecreatinganetforanend-useryoumaywanttogiveanodelikeTbOrCaastyleofHidden.Ifyouwanttohideallthelinks,youcanuseStyle→Links→HideLinks.TheStyle→Fontchoicemaybeusedtochangethefontandsizeofthenodes.MoreInfo

NetTransformation–PARTOFQUICKTOUR

Nodeabsorptionremovesanodewithoutaffectingtheoverallglobalrelationshipoftherestofthenodes(i.e.thejointprobabilitydistribution).

Thissmalldemonstrationofnodeabsorptionwillshowhowitdoesn’teffectthebeliefsoftherestofthenet.Open"Car_Diagnosis_2"fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder.CompileitwithNetwork→Compile,andnoticethatthebeliefis25.4%that“SparkQuality”is“good”.Ifyouenterafindingof“dim”fornode“Headlights”,thebeliefchangesto1.47%.Nowselectnodes“MainFuse”,“BatteryAge”,“VoltageatPlug”and“SparkPlugs”,andthenclickthetoolbarbuttonorchooseModify→AbsorbNodes.Theselectednodes

willbeabsorbed,linkswillbeaddedandremoved,andprobabilitytablesadjustedtomaintaintheglobalrelationship.NowdoNetwork→Compile,andobservethebeliefis1.47%that“SparkQuality”is“good”asitwasbeforetheabsorption.IfyouthendoNetwork→RemoveFindings,thebeliefchangesto25.4%,whichiswhatitwasintheoldnetbeforeanyfindingswereentered.

Linkreversalchangesthedirectionofalinkwithoutaffectingtheoverallglobalrelationshipoftherestofthenodes(i.e.thejointprobabilitydistribution).Selectalinkandthenclickthe toolbarbuttonorchooseModify→ReverseLinks.Neticamayhavetoaddextralinksinordertomaintainthejointprobabilitydistribution(oritmaybeabletoremovesomelinks).

SeealsoDisconnectingandReconnectingLinks

LearningfromData–PARTOFQUICKTOUR

Tutorial:OpentheBayesnetcalled"Car_Diagnosis_0"fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder(note:donotuse"Car_Diagnosis_2").Itisasimplified=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">examplenetcontainingnodesforafewvariablesofinterestwhendiagnosingacarthatisnotrunning.Thenodesarelinkedupinacausalmanner,butthenetdoesnotcontainanyinformationotherthanthenodenames,theirstates,andhowtheyarelinked.Ifyou=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickoneofthenodes,andthenchooseTable,youwillseeinthetabledialogboxwhichappears,thatthenodehasno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsdefined(theemptyboxesintheright-handpanel).Noneofthenodeshaveanyprobabilitiesdefined,sothenetisnotyetreadyfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">inferencebutinthisstepwewilllearntheprobabilitiesfromdata.

Tolearnaprobabilistictableforeachofthenodeswewilluseafileof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">casesofcarspreviouslyarrivingatagarage,called“CarCases”,inthe“Examples”folder.Youmaywanttoexaminethisfilewitha=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditor.Therowofheadingsacrossthetoparethenamesofthenodesinthenet,andeach

possiblevaluetheycantakearethestatenamesofthosenodes.“BatAge”isacontinuousnode,soitsvaluesarerealnumbers.Theasterisks(*)indicatedatavalueswhicharenotknown(i.e.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdata).

Withthenetwindow=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">active,andnonodes=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected(otherwisethelearningwillonlyapplytotheselectednodes),chooseCases→Learn→IncorpCaseFile.Whenyouarequeriedforafile,chooseCarCases,andenter1forthedegree.Neticawillusethecasestolearnprobabilistictablesforeachnodeofthenet,withthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowdisplayingthefractioncompleted.

Whenitisfinished,ifyouexamineafewnodeswiththetabledialogbox,youwillseethelearnedprobabilitydistributions.Youcanclickontheselectorthatsays"%Probability",andchoose"Counts"fromthemenutoseethenumberofoccurrencesofeachpossibilityinthedatafile.FromtheCountstable,Neticageneratesthe"Unnormalized"tablebyaddingasmallconstant(usually1)toeachcell.SummingeachrowoftheUnnormalizedtableresultsinthe"Experience"table,whichisusedtonormalizetheunnormalizedtable,andproducethe"Probabilities"table.Thus,Neticacanlearnthelocalprobabilitytablesinaverysimpleandeffectiveway.Ifyouhave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_latent_node.htm');returnfalse;">latentvariables,orlotsof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdata,thenNeticamustuseconsiderablymorecomplexalgorithms,suchasEMorgradientdescenttolearnthetables.

NowthatthelocalCPTtableshavebeenlearned,youcancompilethenetanddoinference,pastepartsofitintoadecisionnet,absorbnodes,etc.

Ifyouwanttolearnthelinkstructureofyournetbasedonacasefile,usethestructurelearningfeature.

NeticacanalsobeusedtogeneratefilesofcaseswhichfollowtheprobabilitydistributionofaBayesnet(i.e.“sample”fromtheBayesnet).Thesecasescanbeusedasrealisticexamplesofpossiblescenarios,orassyntheticdataforlearningexperiments.Simplyselectthosenodesofthenetforwhichyouwantcolumnsinthecasefile,andthendoCases→SimulateCases.Youwillbequeriedforthenumberofcasestogenerate,thenameofthefiletocreate,andhowmuchmissingdatayouwant(enter0fornone,1forallmissing).

MoreinfoonNetica'sLearning

SeealsoLearningfromanExcelFile

SeealsoTestNetwithCases

Decision-MakingNets–PARTOFQUICKTOUR

WithNetica,decisionnetsarethesameasregular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnets,exceptthattwoadditionaltypesofnodesarepresent,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodesandutilitynodes.InaregularBayesnet,allthenodesarecalled=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenodesbecausetheyhaveonlytodowithmodelingthenatureorrealityoftheworld,thelikelihoodofitsbeinginanyofitspossiblestates.Theconceptofutilityandtheconceptofdecisionareseenasoutsideofmerelydepictingreality,beingmoreintherealmofgoals,desires,andagendas.NeticacompilesbothaBayesnetandadecisionnetintoajunctiontreeforefficiency.

Tutorial:UseFile→Opentoreadthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnet(alsoknownasaninfluencediagram)"Umbrella"fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder.Byopeninga=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogboxforeach=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenode(beigeoval)youcanobserveits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">conditionalprobability

table,andbyopeningoneforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynode(greenhexagon),youcanseeitsutilityfunction.Ifyoulookatthetabledialogboxforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnode(bluerectangle),youwillseethatthenodedoesnotyethaveanyfunctionalrelation,whichindicatesthatthereisnodecisionfunctionassociatedwiththenode.Ourgoalistofinda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_rule.htm');returnfalse;">decisionfunctionwhichwillmaximizethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueoftheutilitynode.

ThisisaccomplishedbychoosingNetwork→Compile.Ifyouthenlookatthetabledialogboxforthedecisionnode,itwilldisplaythediscovereddecisionfunction(youwillhavetoclickthe“Reset”buttonifyoudidn’tfreshlyopenthedialogbox).Thenumbersinthe“Decide_Umbrella”givetheexpectedutilityofeachchoice.Youcan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enterfindingsforForecasttoseehowtheychange.

Ifyouwanttotryanotherdecisionnet,open“Car_Buyer_Neapolitan”,whichisdescribedinNeapolitan90,andisbasedontheclassic“CarBuyer”influencediagram.Itinvolvestwosequentialdecisionsaboutwhethertodosometestsandthenwhethertobuyacertainusedcar.Theoptimaldecisionsturnouttobenottodoanytests(D=none),buttobuythecar(B=BuywhenD=none).

Hereisamoredetailedversionofthisexercise.

EquationsandTimeExpansions–PARTOFQUICKTOUR

Tutorial:OpentheDynamicBayesNetcalled"Bouncing"fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder.Itisdesignedtomodelaballwhichbouncesbackandforthinastraightlinebetweentwoparallelbarrierswithoutlosinganyenergyateachbounce.Initiallywehavenoknowledgeofthepositionorvelocityoftheball.

ThePositionandVelocitynodesstandforthepositionandvelocityateachinstantoftime,andareconnectedtogetherwithbrown=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_time_delay_link.htm');returnfalse;">timedelaylinks(andcouldalsohaveregularblacklinksaswellifdesired).Youcanthinkofatimedelaylinkasdeliveringtothearrowofthelinkthevaluethatthetailhadsomeperiodoftimeago,withthatperiodoftimebeingthelink'sdelay.

Equations:Ifyoudouble-clickonthePositionnodeyoucanseethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equationwhichdefinesthenewpositionintermsoftheoldposition,andthevelocity.Itinvolvestheconstant"dt",whosevaluemaybechanged(byright-clickingonthedtnodeandchoosingEnterNumericFinding)toprovideadifferentamountoftimebetweentimeslices.

Byclickingdownontheselectorthatoriginallysays“Equation”,youcanchoose“Discretization”toseehowthenodehasbeen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretized.Later,youcaneditthislisttochangethediscretization.

Thisnethasalreadyhadit'sprobabilitytables(CPTs)builtfromtheequationateachnode.Ifitdidn'thave,thefirststepwouldbetogenerateprobabilitytablesforthecurrentdiscretizationbymakingsurenonodesareselectedand

choosingTable→EquationtoTablefromthemainmenu.Enter1000whenpromptedforthenumberofsamplespercellandpress‘No’whenaskedaboutincludingsamplinguncertainty.

TimeExpansion:NextyougenerateatimeexpandedversionofthenetbydoingNetwork→ExpandTime.Enter2inthedialogboxfortheexpansiontimeand1fortheburn-intime.Thiswillmakeanewwindowwithanewnetinit.Youwillprobablywanttoresizethiswindowtomakeitwider.YoucanuseLayout→DrawingSizeandmaketheentryblank.ThenewnetisaregularBayesnetwitheachPositionandVelocitynoderepresentingthepositionandvelocityatanewpointintime,withnodestotherightcorrespondingtolatertimes.

FinallywecancompiletheBayesnetforprobabilisticinferencewithNetwork→Compile.Experimentwithsettingthepositionorvelocity(byclickingonthedesiredrange)toindicateobservationsatcertaintimes,andseehowthebeliefsforpositionandvelocityatallothertimeschange.

Aninterestingsituationiswhentheballisneartheboundary,butyoudon’tknowwhichwayitisgoing,sinceafteralittlewhileitwillsurelybemovingawayfromtheboundary(perhapsduetoabounce).Orifthepositionsat2timesareknown,canitinferthevelocity?Orifjustthevelocitiesattwoadjacenttimesareknown,andoneisthenegativeoftheother,canitinfertheposition(becauseitmusthavebounced).Youcanalsotry=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteringsomenegativefindings(thattheballisn’tatsomeparticularpositionorvelocity)byholdingdowntheSHIFTkeywhenyouclickontheinterval.

Rememberthatthenumericalresultswillnotbeexact,duetothediscretizationandsamplingerrorinconvertingtheequationstoprobabilitytables.YoumayalsowanttotryafinerdiscretizationbychangingtheRangesoftheoriginalunexpandednet.

Whenyoubuildyourowntimedelaynets,tomakesomelinksrepresentatimedelay,selectthelinks,thenchooseModify→DelayLinks.Oryoucanusethenodedialogbox,choosing"Delay"fromthemulti-purposeselectoratthebottom.

Seealso:dynamicBayesnets,andtheEquationschapter.

IntroductoryReferencesforBayesNetsandDecisionNetsOverview:ForanoverviewofBayesnetsanddecisionnets,therearetwospecialjournalissuesthataresuitable.Thefirstisthewinter1991editionofAIMagazine,whichcontainsboth“BayesianNetworksWithoutTears”(Charniak91)and“DecisionAnalysisandExpertSystems”(Henrion&BH91).Theotherisvolume38oftheCommunicationsoftheACM,whichisdevotedtoBayesnetsanddecisionnets(Heckerman&MW95),andhasintroductorymaterialanddescriptionsofrealapplications.

Fundamentals:In1988JudeaPearlwroteProbabilisticReasoninginIntelligentSystems(Pearl88),whichwasthemostinfluentialandwidelycitedbookintheformativedevelopmentofBayesnets.Itisanexcellentfoundationalbook,butitdoesn’tcontainthelatestdevelopments,andhasaverymathematicalandtheoreticalorientation.BayesianNetworksandDecisionGraphs(Jensen01)hassomewhatmorerecentresults,althoughtheearlierJensen96maybeevenmoreusefultoabeginnerwhoisjustinterestedinunderstandingandapplyingBayesnetsinabasicway,ifitcanbeobtained.

The"bible"onBayesnetsrightnowisProbabilisticGraphicalModels(Koller&F09).Itisverycomprehensiveandwrittenatahighacademiclevelbytwooftheworld'sleadingresearchersonBayesnets.Inthesamevein,butnotascomprehensive(althoughcoveringsometopics,suchasinference,withgreaterdepth)isModelingandReasoningwithBayesianNetworks(Darwiche09).

Applied:ThebestbookonthetheoryofhowtoapplyBayesnetstotherealworldisBayesianNetworksandInfluenceDiagrams(Kjaerulff&Madsen08).BayesianArtificialIntelligence(Korb&Nicholson04)alsocontainsusefulmaterialtoconstructmodels.Asamplingofreal-worldapplicationscanbefoundinBayesianNetworks:APracticalGuidetoApplications(Pourret&Naim&Marcot08).

FortheusageofBayesnetsinparticularfields,see:

-ProbabilisticMethodsforBioinformatics(Neapolitan09)

-ProbabilisticMethodsforFinancialandMarketingInformatics

(Neapolitan07)

-Ecology:SpecialIssueofCanadianJournalofForestResearch(NRC06)

-PlanningImprovementsinNaturalResourceManagement(Cain01)

-OperationalRisk:MeasurementandModelling(King01)

Russell&N09isanexcellentintroductorytextbookforartificialintelligencethatdoesagoodjobofdescribingBayesnets,decisionnets,dynamicdecisionnets,policyiteration,etc.withintheoverallcontextofintelligentagentsandAIsoftware.

Causality:Averyaccessibleandeasy(butworthwhile)readoncausalmodelsisCausalModels:HowPeopleThinkAbouttheWorldandItsAlternatives(Sloman05).IfyouarebuildingcausalBayesnets,andhaven'thadalotofexperiencewithcausalmodeling,youshoulddefinitelyreadthatbook.Foramoreacademicandadvancedstudyoncausality,readCausality:Models,Reasoning,andInference(Pearl09).Itisbytheworld'sleadingresearcheroncausality,andalthoughitisataveryadvancedlevelforthesubject,youcanselectivelyreadittogetthemostimportantideaswithoutmuchdifficulty.Theexcellentepiloguecanbereadwithnobackgroundknowledgerequired;readitfirst.Forcausalityasappliedtopsychology,seeTheMind'sArrows:BayesNetsandGraphicalCausalModelsinPsychology(Glymour01).

Research:AlthoughmuchoftheliteratureonBayesnetsispublishedwithintheartificialintelligence(AI)community,itisreallythecombinedworkofthestatistics/probability,decisionanalysis,operationsresearch,andAIcommunities(andincreasinglyothercommunitiesthatareapplyingBayesnets,suchasresourcemanagement,ecology,finance,medicine,etc.).ManyoftheresearcherswhodevelopedthetheoryofBayesnetsanddecisionnetsattendedtheannual“UncertaintyinArtificialIntelligence”conferencefrom1985topresent,andsoadvancedmaterialcanbefoundintheconferenceproceedings(availablefromthe"ConferenceProceedings"sectionoftheAUAIsite).

DesignPhilosophyNeticawasdevelopedusingauniquesoftwaredevelopmentprocess.ManyofourclientsaresurprisedatthesmallsizeofNetica,consideringitsadvancedcapabilities,easeofuse,andreliabilitycomparedtootherBayesnetsoftware.Internally,ithasverylittleredundancy(mostmodernWindowsprogramshavealargepercentageofredundantorunusedcode),andanelegantinternalarchitecturedesignedtogivemaximumpowerandusabilityinthesimplestmanner.

Ourdevelopmentprocessemphasizesconstantiterativeimprovement.Everytimeaclientreportsabugorasksaquestion,wehaveaprocessinplacetofixthatbug,ormakesurethequestionisansweredbytheonscreenhelp.Wheneveraclientexpressesfrustrationorgivesusawish-listitem,wemakeaplanonhowtoaddresstheissue,andeithermakeanimmediatechange,oraddittoourshort-rangeorlong-rangedevelopmentschedule.IfyoueverhaveanyproblemwithNetica,frustrationwithhowitworks,ordesireforanewfeature,please=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">letusknow;yourinputwillbeusedtomakeNeticaabetterproduct.

Wehavezero-toleranceforbugsin=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPI.Itgetsthoroughlytestedwithourextensivein-housetestingandbyourlargeclientbaseovermanyyears,andithasnoknownbugs.Thefactthat=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_Application.htm');returnfalse;">NeticaApplicationsharesmuchofitscodewithNeticaAPImeansthatNeticaApplicationhasaverysolid,robustcore.

WekeepabreastofthelatestdevelopmentsinBayesnettheoryandtechnology,andareconstantlyaddingfeaturesbasedonnewresearchresultsfromourresearchandthatpublishedinthegeneralliterature.YouwillfindinNeticamanyexcitingnewfeaturesnotavailableinanyotherBayesnetsoftware.

OneofourdesigngoalsistomakeNeticaveryversatile;itisatoolthatintherighthandscanbeusedformanydifferenttasks.Clientsoftenshowusimaginativesolutionsthey'vecreatedbycombiningvariousNeticafeatures,andmanyhavetoldusthatitwas"fun"touseNeticabecauseofthepoweritgavethem.

BayesNetsandProbabilisticInferenceABayesnet(alsoknownasabeliefnetworkorprobabilisticcausalnetwork)capturesbelievedrelations(whichmaybeuncertain,stochastic,orimprecise)betweenasetofvariables,whicharerelevanttosomeproblem.Theymightberelevantbecausetheywillbeobservable,becausetheirvalueisneededtotakesomeactionorreportsomeresult,orbecausetheyareintermediateorinternalvariablesthathelpexpresstherelationshipsbetweentherestofthevariables.

Example:AclassicexampleoftheuseofBayesnetsisinthemedicaldomain.Hereeachnewpatienttypicallycorrespondstoanew=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">case,andtheproblemistodiagnosethepatient(i.e.findbeliefsfortheunmeasurablediseasevariables),predictwhatisgoingtohappentothepatient,orfindanoptimalprescription,giventhevaluesofobservablevariables(symptoms).Adoctormaybetheexpertusedtodefinethestructureofthenet,andprovidetheinitialrelationsbetweenvariables(oftenintheformof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">conditionalprobabilities),basedonhismedicaltrainingandexperiencewithpreviouscases.Thenthenetprobabilitiesmaybefine-tunedbyusingstatisticsfrompreviouscases,andfromnewcasesastheyarrive.

BayesNetConstruction:WhentheBayesnetisconstructed,one=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodeisusedforeachscalarvariable,whichmaybediscrete,continuous,orpropositional(true/false).Becauseofthis,thewords“node”and“variable”areusedinterchangeablythroughoutthisdocument,but“variable”usuallyreferstotherealworldortheoriginalproblem,while“node”usuallyreferstoitsrepresentationwithintheBayesnet.

Thenodesarethenconnectedupwithdirected=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">links.IfthereisalinkfromnodeAtonodeB,thennodeAissometimescalledthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parent,andnodeBthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">child(ofcourse,Bcouldbetheparentofanothernode).UsuallyalinkfromnodeAtonodeBindicatesthatAcausesB,thatApartiallycausesorpredisposesB,thatBisanimperfectobservationofA,thatAandBarefunctionallyrelated,orthatAandBarestatisticallycorrelated.Theprecisedefinitionofalinkisbasedonconditionalindependence,andisexplainedindetailinareferencelikeNeapolitan90orPearl88.However,mostpeopleseemtointuitivelygraspthenotionoflinks,andusethemeffectivelywithoutconcentratingontheprecisedefinition.

Finally,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">probabilistictablesareprovidedforeachnode,whichexpresstheprobabilitiesofthatnodetakingoneachofitsvalues,conditionedonthevaluesofitsparentnodes.Somenodesmayhaveadeterministicrelation,whichmeansthatthevalueofthenodeisgivenasadirectfunctionoftheparentnodevalues.

ProbabilisticInference:AftertheBayesnetisconstructed,itmaybeappliedtoaparticularcase.Foreachvariableyouknowthevalueof,youenterthatvalueintoitsnodeasa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">finding(alsoknownas“evidence”).ThenNeticadoesprobabilisticinferencetofind=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsforalltheothervariables.Supposeoneofthenodescorrespondstothevariable“Temperature”,anditcantakeonthevaluescold,mediumandhot.Thenan

examplebelieffortemperaturecouldbe:[cold-0.1,medium-0.6,hot-0.3],indicatingthesubjectiveprobabilitiesthatthetemperatureiscold,mediumorhot.

Dependingonthestructureofthenet,andwhichnodesreceivefindingsordisplaybeliefs,Neticamaydodiagnosis,prediction,classification,logic,arithmeticcalculation,oranycombinationofthese,tocompletetheprobabilisticinference.Thefinalbeliefsaresometimescalledposteriorprobabilities(withpriorprobabilitiesbeingtheprobabilitiesbeforeanyfindingswereentered).ProbabilisticinferencedoneusingaBayesnetiscalled=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating.

Ifyouwanttoapplythenettoadifferentcase,thenallthefindingscanbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">retracted,newfindings=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">entered,andbeliefupdatingrepeatedtofindnewbeliefsforallthenodes.

Probabilisticinferenceonlyresultsinasetofbeliefsateachnode;itdoesnotchangethenet(knowledgebase)atall.Ifthefindingsthathavebeenenteredareatrueexamplethatmightgivesomeindicationofcasesthatwillbeseeninthefuture,youmaythinkthattheyshouldchangetheknowledgebasealittlebitaswell,sothatnexttimeitisused,itsconditionalprobabilitiesmoreaccuratelyreflecttherealworld.Toachievethisyouwouldalsodo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probability_revision.htm');returnfalse;">probabilityrevision.

SeealsoLearningfromCases

Netica’sProbabilisticInferenceNeticausesthefastestknownalgorithmforexactgeneralprobabilisticinferenceinacompiledBayesnet,whichismessagepassinginajunctiontree(or“jointree”)ofcliques.ThealgorithmsusedaredescribedinSpiegelhalter&DLC93,Jensen96andNeapolitan90.

Inthisprocess,Neticafirst=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compilestheBayesnetintoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontree.ThejunctiontreeisimplementedasacomplexsetofdatastructuresconnectedupwiththeoriginalBayesnet,butinvisibletoyouasauserofNetica.Youenter=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsforoneormorenodesoftheoriginalBayesnet,andthenwhenyouwanttoknowtheresultantbeliefsforsomeoftheothernodes,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_updating.htm');returnfalse;">deterministicupdatingandthenbeliefupdatingisdonebyamessage-passingalgorithmoperatingontheunderlyingjunctiontree.

ItdeterminestheresultantbeliefsforeachofthenodesoftheoriginalBayesnet,whichitdisplaysasabargraph,oraneedlemeter,ateachnode.Youmaythenentersomemorefindings(tobeaddedtothefirst),orremovesomefindings,andwhenyourequesttheresultantbeliefs,beliefupdatingwillbeperformedagaintotakethenewfindingsintoaccount.

Neticacanalsodoprobabilisticinferencebylinkreversalsandnodeabsorption,butthosearemainlymeantfortransforminganetanddoingmodelexploration,andareusuallynotasfastorasconvenientforgeneralprobabilisticinferenceasthecompiledjunctiontreesdescribedabove.

ExampleBayesNetLet’slookatanexampleofusingNeticatodoprobabilisticinference.Inthisexamplewewillreadinasimplenetfromafile,compileitintoaformsuitableforfastinference,entersomefindings,andseehowthebeliefsofvariousnodeschangewitheachfinding.

Thenetwewilluseisshownbelow.ItisatoymedicaldiagnosisexamplefromLauritzen&S88thathashistoricallybeenusedfordemonstrationpurposes.Toacertaindegree,thelinksofthenetcorrespondtocausation.Thetwotopnodesare“predispositions”whichinfluencethelikelihoodofthediseasesintherowbelowthem.Atthebottomaresymptomsforthediseases.

YoucanreaditintoNeticabychoosingFile→Openfromthemenu(menuselectionsareindicatedinbold,witharrowsindicatingchoicesorsubmenus,sothepreviousmeanschoose“Open...”fromthe“File”menu).Whenthestandardfileopeningdialogboxappears,useittoopenthefilecalled“ChestClinic”.ThisfileisincludedwiththeNeticadistributioninthe“Examples”folder.

Ifyoucompile“ChestClinic”bychoosingNetwork→Compile,youwillseesomethinglikethefollowing:

Thedefaultnodestylehaschangedtobelief-bar,sothedisplaylooksdifferent.Also,theappropriatedatastructuresforfastinferencehavebeenbuiltinternally.Ifyouenterafindingof‘abnormal’fornode“X-RayResult”,byclickingontheword‘abnormal’,thebeliefswillbeautomaticallyupdated,sothatthebeliefthatthepatienthaslungcancergoesfrom5.5%to48.9%.ThenindicatingthatthepatienthasmadeavisittoAsiadecreasesthatbeliefto37.1%,becausetheabnormalXRayispartially=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_explaining_away.htm');returnfalse;">explainedawaybyagreaterchanceofTuberculosis(whichthepatientcouldcatchinAsia).

CompilingaBayesNetTocompilethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activeBayesnet,chooseNetwork→Compile,orclickthe toolbarbutton.Iftheyaredimmedthencompilinghasalreadybeendone.A“=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontree”forfastinferencewillbebuiltinternally.Thedefaultdisplaystyleforthenodeswillbechangedtobelief-bar,soifthenodeshaven’thadtheirdisplaystylesset,thentheywillbedisplayedinbelief-barstyle.

Forsmallnets,theCompilecommandwillseemtoperforminstantly.Forlargenetsitmaytakeafewseconds,inwhichcasetheprogresswillbedisplayedinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindow.

Auto-Compile:Ifyousaveacompiled=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_auto_update.htm');returnfalse;">auto-updatingnettofile,thenthenexttimeyouopenit,Neticawillautomaticallycompileitandperformupdating.Ifthenetisnotcompiledwhenyousaveit,thenyoumustcompileitasdescribedabovewhenyounextopenit.Ifyouwishtoreadinanauto-compilingnetwithoutperforminganycompiling,holddowntheSHIFTkeywhenyouopenit.

MissingTables:ItispossibletocompileandupdatenetswhoseCPTsorutilitytablesareabsentorincomplete.Neticatakesmissingentriesasuniformprobabilitiesorzeroutilities.Iftherearemissingentriesortables,thenwhilecompilingNeticawillbeepandputamessage(#2760)intheMessageswindow.

Optimized:NeticaalsohasaNetwork→CompileOptimizecommand,whichspendsalongtimeworkingoutaveryefficientstructurefortheinternal

junctiontree.Asitisworking,itdisplaysintheMessageswindowthememoryrequirementsandprojectedinferencetimetodoabeliefupdatingwiththebeststructureithasdevelopedsofar.PresstheCTRLkeyandholddowntheleftmousebuttonatthesametimewhenyouwantNeticatostopandusethatstructure.

Thememoryrequirementsitdisplaysareveryaccurate,butwhenconsideringtheinferencetimekeepinmindthatitisbasedondoingtheinferenceusingthesamecomputerastheonedoingthecompiling,itassumesthecomputerhasenoughRAMmemoryinstalledthatitdoesn'tneedtousevirtualmemory,andthatithasalargeshareoftheprocessortimeundermultitasking.Italsodoesn'tincludethescreenredrawtime,whichdependsonhowlargetheBayesnetwindowis,andonthedisplaystyleofthenodes.

IfyousaveaBayesnetafteranoptimizedcompile,thenthenexttimeyouopenitthequickcompilecommandwillgiveittheoptimizedstructurequickly(aslongasyoudon’tchangethenetnodesorlinksinbetween).

Technical:Forthoseinterestedinatechnicalexplanation,thequickcompiledoesaminimum-weightsearchforagoodeliminationorder,andtheoptimizedcompilesearchesforthebesteliminationorderusingaspecializedalgorithmwhichisacombinationofminimum-weightsearchandstochasticsearch(withsomefacetsofmulti-startmethods,simulatedannealingandgeneticalgorithms).

EnteringandRetractingFindingsPurpose:Usuallyyouenterfindings(sometimescalled“evidence”)totemporarilyapplya=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnettoaparticular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">casefor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">probabilisticinference.

Entering/Right-click:Toenterafindingforanode,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonitandchooseEnterFinding.Eachpossiblestateofthenodewillbelistedinalphabeticalorder;choosethefindingfromit.Menuitemsappearasstatetitle(orbystatenameifnotitlesexist).

Afterthefindinghasbeenenteredthenodewillbedarkened(oritscolorotherwisechangedasdefinedbynode-sets).Itdoesnotmatterinwhatorderyouenterasetoffindings.

Entering/Left-click:Whenthenetis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compiledandthenodeisdisplayedinbelief-barormeterstyle,left-clickdirectlyonthenameofthefindingyouwishtoenter.Ifthenodeisdisplayedinbelief-barstylethenasolidoutlinedbarisdrawnforthestatematchingthefinding.

Whenyouenternewfindings,andbeliefupdatingisnotyetdone,onlythosenodeseffectedwillhavetheirbeliefsindicatedinvalid.

Retracting:Ifyouwishtoretract(i.e.remove)afindingthatyouhaveenteredforsomenode,chooseUnknownfromitsfindingsmenu,orclick

againdirectlyonthenameofthefindingofabelief-barnode.Enteringafindingandretractingitisequivalenttoneverhavingenteredit,eveniftherewereotherfindingsenteredinbetween.

Anotherwayofretractingthefindingsforsomenodesisto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthemandthenchooseCases→RemoveFindings,orclickthetoolbarbuttonwitharedcrossoverthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case_symbol.htm');returnfalse;">casesymbol:

Ifyouwishtoretractallthefindingsenteredforallthenodesinthenet,makesureallornoneofthemare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,andthenchooseCases→RemoveFindings.Thisisusefulifyouarefinishedwithonecaseandwishtomoveontoanother.

MultipleNodes:Youcanenterthesamefindingforawholesetofnodesatonce.Firstselectthem,thenright-clickononeoftheselectednodes,andproceedasabove.MoreInfo

Uncertain:Ifyouwanttoenterafindingthatanodeisnotinaparticularstate,oryouwanttoenteranuncertainfinding,youwouldenteritasanegativeorlikelihoodfinding.

Consistency:Neticacanchecktheconsistencyofthefindingsyouenter.

SetsofFindings:IfyouhavemultiplefindingstorepeatedlyenterintoaBayesnet,youcanputtheminacasefile.

DecisionNodes:Enteringafindingintoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodedoesnotreallycorrespondtodiscoveringinformationormakinganobservation,butrathertocommittingtoadecisionchoice.Nevertheless,itisstilloftenlooselyreferredtoas"enteringafinding".

BeliefUpdatingandAutoUpdatingWhenprobabilisticinferenceisdoneusingaBayesnet,itiscalledbeliefupdating.New=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefs(posteriorprobabilities)arefoundforeachofthenodestoreflectthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingscurrentlyenteredinthenet.

Auto-Updating:NormallyNeticadoesbeliefupdatingquicklyandautomaticallyaftercompiling,andeverytimeafindingis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">entered.However,itcanbeslowonlargenets,soyoumaywanttoenterseveralfindingsatoncebeforeupdating(youalsomaywanttousetheoptimizingcompiler).Inthatcase,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggleoffNetwork→AutomaticUpdating,enterthefindings,andeachtimeyouwanttoupdatethebeliefschooseNetwork→Update,orclickthe toolbarbutton(theywillbedimmedifbeliefupdatingisnotcurrentlyrequired,orifthenetisnotcompiled).

NothingHappens:Ifyouenterfindingsintoanet,andnobeliefupdatingoccurs,perhapsitisbecause=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_auto_update.htm');returnfalse;">auto-updatingisoff(thestateofauto-updatingissavedwitheachnetfile)orthenetisnotcompiled.

DimmedBeliefDisplay:Ifauto-updatingisturnedoff,andyouenteranewfinding,orifnofindingsareenteredbutbeliefupdatingwasneverdone,thenthebelief-barsormeterswillnotdisplayvalidresults,andsotheyaredrawndimmedoringrayratherthaninsolidblack.Thereasontheyarenotremoved

completelyisthatyoumaywanttoseewhatthebeliefswereatthepointofthelastbeliefupdating.

NegativeandLikelihoodFindingsNegativeandlikelihoodfindingsare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingswithsomeuncertaintyattached.

Negative:Apositivefindingisknowledgethatsomevariabledefinitelyhasaparticularvalue.However,youmayknowthatthevalueofanodeisnotsome=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">statewithoutknowingwhatitsvalueis.

Thisiscalledanegativefinding.Forexample,saythenode“Temperature”cantakeonthevaluescold,medium,andhot.Youmayobtaininformationthatthetemperatureisnothot,althoughitdoesn’tdistinguishbetweenmediumandcoldatall.Thatisasinglenegativefinding.

Ifyoureceiveanothernegativefindingthatthetemperatureisnotmedium,thenyoucanconcludethatitiscold.Soseveralnegativefindingscanbeequivalenttoonepositivefinding.

Likelihood:Athirdtypeoffindingisalikelihoodfinding(alsoknownas“virtualevidence”).Inthiscaseyoureceiveuncertaininformationaboutthevalueofsome=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenode.Itcouldbefromanimperfectsensor,orfromafriendwhoisnotalwaysright.

Sayyouhaveathermosensortomeasure“Temperature”,whichisdesignedsothatwhenthetemperatureishotitissupposedtoturnon.Inactualpracticeyoufindthatwhenthetemperatureiscoldthesensornevergoeson,whenthetemperatureismediumitgoeson10%oftime,andwhenitishotitalwaysgoeson.Ifatacertaintimeyouobservethesensoron,andwantto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enterthisfindingintotheTemperaturenode,thenyoudosoasalikelihoodfinding.

Alikelihoodfindingconsistsofoneprobabilityforeachstateofthenode,whichistheprobabilitythattheactualobservationwouldbemadeifthenodewereinthatstate.Forourtemperatureexample,thelikelihoodfindingwouldbe(0,0.1,1).Acommonmistakeistothinkthatthelikelihoodistheprobabilityofthestategiventheobservationmade(inwhichcasethenumberswouldhavetoaddtoone),butitistheotherwayaround.

Entering:Youcanenteranegativefindingforabelief-barnodeofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compilednet,byholdingdowntheSHIFTkeywhileyouclickonthenameofthefindingyouknowitsnot.Youcanenteralikelihoodfindingforanodebychoosing“Likelihood”fromits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_findings_menu.htm');returnfalse;">findingsmenu.Youwillthenbequeriedforthelikelihoodnumbers.

Youcanenteranegativefindingbyenteringalikelihoodfindingconsistingofall1s,exceptasingle0forthestatethatyouknowit’snot.Byhavingmorethanasingle0youcanenterseveralnegativefindingsatthesametime.

Accumulating:Wheneveryouenterapositivefindingforanode,alltheoldfindingsforthatnodeareautomatically=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">retractedfirst.However,ifyouentermorethanonelikelihoodfindingforanode,youwillbequeriedifyoufirstwantthepreviousfinding(s)toberemoved,orifyouwantthemtoaccumulate.Bylettingthemaccumulateyoucanenterseveralindependentpiecesofevidence(e.g.imperfectobservations)forthesamenode.Iftheyarenot=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditionally_independent.htm');returnfalse;">conditionallyindependentgiventheobservednode,anditistooinaccuratetoapproximatethemasindependent,thentheyshouldbeenteredby

adding=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">childnodestotheobservednode(oneforeachobservation),connectingthemtogethertoshowthedependency,andthenenteringpositivefindingsforthechildnodes.

Locating:Tofindallthenodeswithnegativeorlikelihoodfindings,useEdit→SelectNodes→LikelihoodFindings.

ConsistencyofFindingsTherearethreewaysthat=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingscanbeinconsistent:

1.Severalfindingsfordifferentnodescanbeinconsistentwitheachother.Thisisthemostcommonformofinconsistency.WhenNeticaalertsyouthatfindingsareinconsistent,thenitmeansthataccordingtothisBayesnet,itisimpossibletoobservethesetoffindingsyouhaveentered.Ifyouknowthatthosefindingsarepossible,thenthefaultliesinthenet’s=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">conditionalprobabilities(seebelow).

2.Severalfindingsforthesamenodecanbeinconsistentwitheachother.Thisonlyappliestofindingsenteredinaccumulationmode,becauseotherwiseeachnewfindingwillretractthepreviousoneforthatnode.Usuallyonly=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativeor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">likelihoodfindingsareenteredinaccumulationmode,andtheonlywaytheycanbeinconsistentistohaveatleastonenegativefinding(orzerolikelihood)foreverystateofthenode.

3.Asinglefindingcanbeinconsistentwiththenetitself.Thisisrare.Basicallythenethasazeropriorprobabilityforthatfinding,whichmeansitisafindingwhichshouldneveroccur.Usuallythisindicatesthenetwasnotdesignedtohandlecasesofthistype.

WhenDetected:Neticawillalwaysdetectaninconsistencyoftype2,andusuallyoftype3,assoonasyoutrytoenterit.During=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingallinconsistencieswillbedetected,andNeticawillreportthem(eithertothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindoworwithadialogbox).Soifthebeliefsarekeptcurrentbybeliefupdatingaftereachfindingisentered(whichisonereasontouse=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_auto_update.htm');returnfalse;">auto-updating),thenyouwillbealertedassoonasyoutrytoenteraninconsistentfinding,otherwiseyouwon’tbealerteduntilthenextbeliefupdatingisinprogress.

Recovery:IfNeticareportsaninconsistentfinding,simply=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">removeitandcontinue.NothingwithinNeticawillbeleftinaproblematicstate.

BeforeEntering:Youcanalwaystellifafindingwillbeinconsistentbeforeyouenteritbylookingatthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefforthatstate(dobeliefupdatingfirstifnecessary).Ifthebeliefiszero,thefindingwillbeinconsistent,otherwiseitwillbeconsistent.

IncorrectNet:Ifyouhaveproblemswithconsistency,re-examinewhether=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">conditionalprobabilitiesyouhaveenteredas0%shouldreallyindicateabsolutelyimpossible.Ifthereissomeverysmallprobabilitythattheyaren'timpossible,thenenterthatverysmallprobabilityinstead.Equivalently,perhapssomenodesthatare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicshouldreallybeprobabilistic.Alsoconsiderthepossibilitythatthenetiscorrect,butthatthefindingsshouldbehigh=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">likelihoodfindings,ratherthan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefindings.

InconsistentNet:Anetcanneverbeinconsistentwithitself.Nomatterwhatitsstructure,orits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">conditionalprobabilitytables,italwaysrepresentssomejointprobabilitydistribution.Onlyfindingscanbeinconsistent.However,anetmaybeincorrectlydesigned,asdescribedabove.

MostProbableExplanationGivenfindingsforsomenodes,youmaywanttofindthemostprobableconfigurationofvaluesfortherestofthenodes.Thiscanbethoughtofasprovidingaplausibleexplanationfortheobservedfindings,andiscalledthemostprobableexplanationorMPE(itisaspecialcaseofthemaximuma-posterioriprobability,orMAP).

YoucannotdeterminetheMPEsimplybytakingforeachnodethestatewithhighestbeliefafterregularbeliefupdating(whichfindsthemarginalposteriorprobabilityforeachnode).Forexample,inalotteryforwhichweknowthereisonewinner,itmightbemostprobableforeachindividualpersontolose,butthentheoverallconfigurationwouldhaveeverybodylosing,whichcontradictstheonewinnerevidence.FindingtheMPEwouldselectonerepresentativepersontowin(perhapswhoboughtthemosttickets),andtherestwouldbelosers.

NeticacanbeusedtofindtheMPE.ToindicatethatyouwishtodoMPEupdatingforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenet,insteadofregularbeliefupdating,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggleNetwork→MostProbableExpl.YouwillhavetorecompileafterturningMPEonoroff,asisindicatedbyallthebelief-barsturninggray.Youthen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enterfindingsintheusualwayanditdoesMPEupdatingimmediatelyafterwardsifNetwork→AutomaticUpdatingison,orotherwisejustafteraNetwork→Updatecommand.

Afterupdating,eachnodewillhaveabelief-baratthe100%level,andusuallysomebarsatlowerlevels.Youcanreadoffthemostprobableconfigurationbytakingforeachnodethestatewiththebaratthe100%level.Theshorterbarsindicatetherelativeprobabilitiesoftheotherstatesgiventhattheothernodesareinthemostprobableconfiguration(scaledbythesamefactorusedto

bringthelongestbarto100%).

Ofcoursethebarsdon’taddto100%,soifyouareeverusingNeticaandareconfusedthateverynodehasa100%barandtherearealsosomeothernonzerobars,itisbecauseMPEupdatingison.ToavoidthepossibilityofaccidentallydoingMPEupdatingwhenregularupdatingisexpected,allnetsstartwiththeMPEfeatureturnedoff,evenifMPEwasonwhenthenetwaslastsaved.

Multiple100%Bars:Sometimestwoormorestatesofthesamenodehavebarsthatareatthe100%level.Thisindicatesthatthereismorethanoneconfigurationwiththehighestprobability(i.e.,theconfigurationshaveequalprobability).Ifmorethanonenodehasthis,thenyoushouldchooseoneofthestatesandenterartificialevidencethatthenodeisinthatstate,toseehowitchangesthemultiple100%barsofothernodes.Bytryingeachofthepossibilitiesyoucanmapoutalltheconfigurationsthatareatthehighestprobabilitylevel.

Problems:YoumustbecarefulusingtheMPE.Generally,itisnotasgoodasposteriorprobability(i.e.regularupdating)fordecisionproblems,orprovidingpredictionordiagnosisprobabilities.Itsresultscanchangewiththeintroductionofirrelevantvariables.And,itcanbedeceptiveinsituationswhereeventhemostprobableexplanationisextremelyunlikely.

WhentoUse:TheMPEisusefulforexplainingandaidingunderstanding.Ifanagentfindstheresultsofregularbeliefupdatingquestionable,andasksyoutoprovideascenarioforwhichthebeliefsareupheld,youcanusetheMPEtofindthatscenario.Peoplesometimesfindacompletelyspecifiedscenarioeasiertounderstand.AndsometimesyoucangaininsightsbyputtingtheBayesnetinMPEmode,enteringtheevidence,observingthemostprobableconfiguration,andthenexperimentingwithaddingextra“evidence”toexploreasetofprobableconfigurationsclosetothemostprobableone,whileseeinghowchangingonenodeeffectstheothers.

CreatingBayesNetsandDecisionNetsThefollowingareactionsyoucantaketocreateanewBayesnetordecisionnet,ortomodifyanexistingone:

•OpeningaWindow•AddingNodes•AddingLinks•UndoingandRedoing•SelectingNodesandLinks•MovingNodesandAutoGrid•ReshapingaLink•SavingaNettoFile•DeletingNodesandLinks•Cut,Copy,PasteandDuplicateNodes•Right-Clicking•ChangingNodeProperties•PlacingTextonNetDiagrams•DocumentationWindow•DrawingSizeandScrolling•ZoomingInandOut•Search/Find•RelatedNodesandLinks•OneOperation,MultipleNodes•EnteringNodeProbabilityTables

OpeningaWindowThefirststepincreatinganewnetistobringupawindowforit.UseFile→New→Networkorclickthe toolbarbutton.Awindowwillappearinwhichyoucanbuildthenet.Thetitleofthewindowwillbesetwhenyousaveittofile.

ExistingNets:Youwilloftenfinditeasiertobuildanetbymodifyinganexistingone.Todoso,readintheexistingonewithFile→Open(orclickthe toolbarbutton),saveitunderthenameofthenewnetwithFile→SaveAs,andthenmakethedesiredmodifications,occasionallysavingitwithFile→Save,orbypressing .Alternatively,youcanreadinarecentlyusednetbychoosingFile→RecentFiles.

Multiple:Youcanopenasmanynetandtextwindowsasyouwish.AswithanyMicrosoftWindowsapplication,thecurrentoperationalwaysappliestotheactivewindow,whichistheoneinfrontwiththenon-dimtitlebar.Youcanmakeawindowactivebyclickingonanexposedpartofit,orbychoosingitstitlefromtheWindowmenu.

Toobtainmultipleversionsofthesamenet,right-clickonthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchooseDuplicateinNewWindow,orchooseWindow→DuplicateNet.

Arranging:FromtheWindowmenuyoucanalsochooseTileorCascade,whichwillarrangeallthewindowsaccordingly.Ifthesearefunctionsyouusefrequently,youcancustomizethetoolbarbyaddingtheirbuttons: ,and ,orsimplyusetheirshortcutkeys.

Closing:Whenyouaredonewithawindow,youcancloseitinoneofthreeways:1.byclickingthe buttoninitstitlebar,2.ifyouhavemadeunsavedchangestoanywindow,Neticawillaskifyouwanttosavethemfirst.MakeittheactivewindowandthenchooseFile→CloseAll,or

3.bypressingCTRL+F4,CTRL+QorCTRL+W.

Ifyoufindtherearetoomanywindowsopenatonce,youcanchooseWindow→CloseAllandbeginanew.

AddingNodesThetoolbarbuttons , and areusedforadding=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenodes(i.e.“chance”or“deterministic”nodes),=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodes,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynodes(alsoknownas“value”nodes)respectively.Whenyouclicktheappropriatebutton,andthenmovethecursoroverthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenetwindow,itwillchangetotheshapeofthenodetobeadded.Nextclickontheplaceinthewindowwhereyouwantthenodetoappear,anditwillbeaddedthere,withthecursorreturningtonormal.

AlternateAddingOptions:Besidesthetoolbar,youcanaddnewnodestoyournetinthefollowingways:1.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">Right-clickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchooseModify→NewNodeandchoosethedesirednodetypefromthelist.Formoreinfo,seebelow.

2.UsingtheOverheadmenu,chooseModify→AddtoaddaNature,Decision,Utility,orconstantnode,ortoaddanewlink.3.Useashortcutequivalent.

Multiple:Toaddaseriesofnodes,double-clickonthetoolbarbuttonforthe

typeofnodesyouwishtoadd,ordouble-pressF9(i.e.pressittwiceinquicksuccession).Thecursorwillchangetotheshapeofthenodeasbefore,butnowitwillbedarkenedindicatingthatanumberofnodesmaybeaddedinaseries.

Toexitthisnode-addingmode,clickthenode-addingbuttonagain,orpressthenode-addingFXkeyagain,orclickthe button,orpressthePause/Breakbutton(orclickonadifferentnode-addingbuttonorpressadifferentnode-addingkey).

NodeTypes:Oftenthemostusefulwaytoaddnodesisby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clicking,becausethenyoucanchoosewhattypeofnodetoadd,insteadofsettingitlater(throughthedialogbox).

Nature-DiscreteDEFINITIONNature-BooleanDEFINITIONNature-NumericContinuousCONTINUOUSVS.DISCRETENature-NumericDiscreteDecisionDEFINITIONDecision-BooleanUtilityDEFINITIONConstantDEFINITION

Properties:Whenanodeisfirstaddeditwillbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selected.WheneveranodeisselectedyoucanpresstheENTERkeytobringupadialogboxforsettingnodeproperties,andwhenthedialogboxfirstcomesup,itsfieldforsettingthenode’snameisselectedforchanging.Thismakesitpossibletoquicklyaddanodewithacertainname.Justclicktheappropriatelyshapedcursorwhereyouwantthenodetobe,presstheENTERkey,typethename,andthenpresstheENTERkeyagain.Thereisnoneedtothinkaboutthedialogboxorwaitforittobefullydrawn.

NodePalette:YoucanusetheNodePalettetostorenodesthatyouuse

frequently.Tostoreanode,copyitandchooseWindow→NodePalette,whichwillbringupawindowtopastethenode.WheneveryouuseNetica,youcanopenthenodepalettetoretrieveyourstorednodes.

NodeGroups:Tohelpwithvisualorganization,youcangroupnodestogether,toformnode-sets.

DeletingNodes:Ifyouwanttodeleteanodefromyournet,youcansimplyhighlightitandpresstheDELETEortheBACKSPACEbuttons.However,ifthenodewaslinkedtoothernodes,therearesomethingstoconsiderbeforedeletingitentirely,asitsdeletioncouldaffectyourCPTs.MoreInfo

AddingLinksToaddalinkfromonenodetoanother,firstclickthe toolbarbutton,chooseModify→Add→Link,orpresstheF10key.Whenyounextmovethecursortothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenetwindow,itwillchangetoalinkshapeindicatingthatitisreadytoaddalink.Clickonthenodethatyouwishtobethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parent,andthenclickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">childnode.Alternately,youcanclickdownontheparent,andwhileholdingthemousebuttondown,movetothechildandthenreleaseit.Thelinkwillappear.Ifyouwant,youcanthenchangetheshapeofthelink.

Adding-Mode:Toaddaseriesoflinks,double-clickthe button,ordouble-presstheF10button(i.e.pressittwiceinquicksuccession).Thecursorwillchangetoalinkshapeasbefore,butnowitwillstaythatwayasyouaddmultiplelinks.Toexitthislink-addingmode,clickthe buttonagain,orpresstheF10keyagain,orclickthe button(orclickonanode-addingtoolbuttonorpressanode-addingkey).

SeveralatOnce:Toaddlinksfromonenodetomany,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_link.htm');returnfalse;">selectallthenodesyouwantthelinkstogoto,thendrawalinkfromthedesiredparenttooneofthem,andallthelinkswillbecreated.

Toaddlinksfrommanynodestoone,selectallthenodesyouwantthelinkstocomefrom,thendrawalinkfromoneofthemtothedesiredchild,andallthelinkswillbecreated.

Deleting:Todeletelinks,simplyselectallthelinksyouwishtodelete,andthenpresstheDELETEkeyorchooseEdit→Delete.Alternately,youcan=4

&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonalinkandchooseDelete.

OverlappingandCycles:Itispossibletoaddmorethanonelinkbetweenthesametwonodes,ortocreate=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_cycle.htm');returnfalse;">directedcycles.FormostBayesnetwork,youdon'twanttodoeitherofthese,andsoNeticawillbeepandputawarninginthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindow(itdoesn'tstopyou,sincethesemaybevalidoperationswhencreatingaDBNornetfragment,butifyoutryto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compilethenetitwillgiveyouanerrormessage).Toremoveanoverlappinglink,justclickonitandpresstheDELETEkey;youmightnotnoticeitdisappearing,sinceafteritisgone,youwillstillseethelinkunderit.

Right-clickingOptions:Foranunselectednode,youcanright-clickonitandchoosetoAddLinkToorFromanyoftheothernodesinthenet.

Onceyouselectanodeorgroupofnodes,right-clickingwillallowyoutoaddlinksToorFromanyothernodeinthenet.Ifagroupofnodesisselected,youcanalsoright-clickonanunselectednodeandchoosetoLinks→AddLinkToorFromSelectedNodes.MoreInfo

UndoingandRedoingWhilebuildingorchangingthenet,youcanundothelastoperationbychoosingEdit→Undo,orpressingCTRL+Z,orclicking ,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchoosingModify→Undo.

Multiple:Toundooperationsprevioustothatone,repeatedlyinvokeEdit→Undo(orCTRL+Z,or ).

Redo:Afteraseriesofundos,youcan“redo”oneormoreofthembyrepeatedlychoosingEdit→Redo,orpressingCTRL+SHIFT+Z,orclicking ,orright-clickingthenetbackgroundandchoosingModify→Redo.

HowMany:Neticawillsaveagreatmanyofthepreviousstepsforundoing,butthiswillbereducediftheyarestepswhichtakelargeamountsofmemory.

Dimmed:IfyouareundoingoperationsandtheEdit→Undomenuitemortoolbarbuttonturnsdim,itmeansyouhaveundonealltheoperationsthatNeticahasremembered.Ifyouareredoingoperations,andtheEdit→Redomenuitemortoolbarbuttonturnsdim,itmeansthatyouhaverestoredalltheoperationsthatwerepreviouslyundone.

PastFileSave:Youmayevenundooperationsthatweredoneprevioustothelasttimethenetwassavedtofile.Asyouareundoingoperations,atthepointthatthenetmatcheswhatwaslastsavedtofile,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_changed_indicator.htm');returnfalse;">changed-indicator*willdisappear,andafterundoingfurtheroperations,itwillreappear.Then,ifyoustartredoingoperations,onceagainitwilldisappearwhenthenetmatchesthefile,andthenreappear.

OtherWindow:Theoperationsdoneineachwindowareremembered

separately,soifyoureturntowindowAafterworkinginanotherwindowforawhile,youcanstillundooperationspreviouslydoneinwindowA.

SelectingNodesandLinksManyoperationsonnodesaredonebyfirstselectingoneormorenodes,andthenchoosingtheoperationtodo.Neticaindicatesaselectednodebydrawingitwithnegativecolors.

SelectingSingleNodes:Selectanodebyclickingonceonit.Youmayhavetoclickonthenode'stitleifclickingonotherpartsofitcausesomeactiontooccur.Otherwise,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickoveranodeandchooseSelect.

SelectingMultipleNodes:Clickdownonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandthendragtheselectionrectangletoincludeatleastapartofeachnode.ChoosingEdit→SelectNodes→All(orpressingCTRL+A)willselectallthenodesinthenet.Tounselectallthenodescurrentlyselected,justclickonceonthenetbackground.

Modifying:Whenyouselectnewnodes,anynodesthatwerepreviouslyselectedwillbecomeunselected,unlessyouholddowntheCTRLkeywhileclickingordragging.Inthatcasetheselectedstatusofthenewnode(s)willbereversed,allowingyoutoaddto,orremovefrom,thecollectionofselectednodes.Anotherwayistoright-clickonanodewhoseselectionstatusyouwishtochange,andchooseSelectorDeselect.

Repeating:Ifyouoftenneedtoselectthesamesetofnodes,youcansetthemasanode-set,andthenselectthembychoosingEdit→SelectNodes→InNodeSet.

Reversing:Toreversetheselectionsothatitconsistsofonlythenodescurrentlynotselected,pressCTRL+SHIFT+AorchooseEdit→SelectNodes→InvertSelection.

ByProperties:Alternatively,youcanselectnodesandlinksaccordingtotheirpropertiesorrelationships.Forexample,youcanselectnodeswithequations,findings,dependenton,parents,ancestors,childrenanddescendents

ofselectednodesbychoosingEdit→SelectNodes…

FromText:Edit→SelectNodes→ListedinClipboardwillselectallthenodeswhosename(nottitle)appearsinthetextcurrentlycopiedtothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboard.Forexample,ifyourwordprocessingprogramhasadocumentthatmentionsseveralnodesbyname,youcouldselectthattext,copyit,andthendoSelectNodes→ListedinClipboardinNeticatoselectthem.

Save/Restore:YoucansavethecurrentselectionastextwithReport→ListofSelected(moreinfo),andthenrestoreitusingEdit→SelectNodes→ListedinClipboard.

Doesn’tWork:Ifyouareselectingbelief-barormeterstylenodes,thenyoushouldclickonthetitle(orname)ofthenode,sinceclickingelsewheremaybeinterpretedas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteringafinding(inwhichcasethenodewillbedarkenedinsteadofdrawnwithnegativecolors).

Links:Toselectalink,clickdirectlyonit.Itwillbecomedrawninhilitedoutlineform.Aswithnodes,iftheCTRLkeyishelddownwhileclicking,itwillreversetheselectionstatusofonlythelinksbeingclickedon,whichcanbeusedtoaddorremovefromyourcollectionofselectedlinks.Youcanalsoright-clickdirectlyonalinkandchooseSelectorDeselect.

Note:Linkscannotbeselectedbydraggingtheselectionrectangleoverthem.Nodesandlinkscannotbothbeselectedatthesametime,sowheneveryouselectlinks,anynodesthatareselectedwillbecomeunselected,andvice-versa.

MovingNodesandAutoGridTomoveanode,clickdownonit,dragittoitsnewposition,andthenreleasethemousebutton.Ifyouwishtomoveasetofnodesandthelinksbetweenthem,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodesyouwishtomove,thenclickdownononeofthemanddragthesettothenewdesiredlocation.

Thereisanunderlying“grid”ofpositions,andwhenyouaddormoveanode,thenodewillbeshiftedslightlysothatitscenterisdirectlyoveroneofthesegridpositions,providingtheAutoGridisturnedon.Thisallowsyoutoquicklydrawanetwhosenodesareperfectlyaligned,andwithlinksrunningperfectlyhorizontalorperfectlyvertical.ToturnAutoGridofforon,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggleLayout→AutoGrid.Ifyouwanttochangethespacingofthegrid,tomakeitfinerorcoarser,chooseLayout→GridSpacing,andadialogboxwillappearallowingyoutomakethesetting.

ToreturntotheoriginalspacingwhenanetisdevelopedwithAutoGridturnedoff,orifchangesaremadetogridspacing,chooseLayout→SnapToGrid.

Nudging:Sometimesitisusefultobeabletomoveanode,orsetofnodes,asmallpredictableamount.Youcanusethearrowkeystodothisnudging.Simplyselectthenodesyouwishtomove,andthenpressthekeywiththearrowinthedirectionyouwantthemtomove.Thedistancetheywillbemovedwitheachpressofthekeyisthegridspacing(providingtheAutoGridisturnedon),soyoucanadjustthisamountusingtheLayout→GridSpacingmenuentry.IftheAutoGridisturnedoffthentheywillbemovedthesmallestperceptibleamountwitheachpressofthekey.

Itisalsopossibletomoveorreshapealinkbyasmallpredictableamount(MoreInfo).

Alignment&Spacing:Toaidwithvisualcomprehensionofyournet,orwheneditinganet,usetheSpaceEvenlyandAlignfeaturesintheLayout

menu.Ifyouareworkingwithalargenet,orareinmultiple-addingmode,youcanquicklyandevenlyspaceoutaroworcolumnofnodes.First,decidewhetheryou’dlikethenodestobespacedByGaps,ByCenters,ByLeft/TopEdges,orbyUsingtheGridandselectthatoptionbychoosingLayout→SpaceEvenly.Next,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthedesirednodesandagainchooseLayout→SpaceEvenly,thistimechoosingspacingofeitherVerticallyorHorizontally.

Similarly,youcanquicklylineuprowsandcolumnsofnodes.YoucanalignnodesByCenters,ByLeft/TopEdges,orByRight/BottomEdgeswhenyouchooseLayout→Align.Then=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodestobealigned,chooseLayout→AlignagainandclickonRoworColumn.

Formoreinfoonimprovinganet’svisualappearance,seedisplaystyle.

ResizingtheNet:IfyouwouldliketochangethespacingoftheentirenetyoucanchooseLayout→SpreadOut/Compact.Enteringanynumbergreaterthan100,inthedialogboxthatcomesup,willspreadouttheentirenet,whilenumberslessthan100willcompactit.Thisoperationonlychangesthespacingbetweenthings,withoutalteringtheirsize.Byselectingsomenodespriortotheoperation,onlythosenodeswillbemoved.

ReshapingaLinkWhenanetdiagrambecomeslargeitcanbeverydifficulttoviewifallthelinksbetweenthenodesarestraightlines.Evensmalldiagramscansometimesbemademorelegiblebychoosingsuitablepathsforthelinks.

AddingBends:Toshapealink,firstclickonceonthelinktoselectit.Thelinkwillbedrawnwiththehilitecolorsurroundingit.Thenclickdownagainontheselectedlink,anddragthecursor.Abendwillbeplacedinthelinkanddraggedbythecursor.Youcanrepeatthistoaddasmanybendsasyouwish.

MovingBends:Tomovethepositionofabend,firstselectthelinkasbefore.Thelinkwillbecomehilitedandtherewillbeasquareboxateachofitsbends,andatitstwoendpoints.Tomoveabendoranendpoint,clickdowninitshilitedbox,dragittoitsnewposition,andthenreleasethemousebutton.

RemovingBends:Movingonebendintoanother,orintoanendpoint,willcombinethem,whichcanbeusedtoremovebends.Ifyouwishtoimmediatelyremoveallthebendsinsomelinks,selectthemandchooseLayout→StraightenLinks.Ifnolinksareselectedwhenyouperformthisoperation,allthelinksinthenetwillbestraightened.Anothermethodistoright-clickdirectlyonalinkandchooseStraighten.

MovingEnds:Therearesomespecialconsiderationswhenmovingtheendpointsofalink.Thearrowendofalinkcannotbedraggedveryfarfromthenodeitpointsto(ifyoutryto,thearrowwilljustbumpagainstaninvisiblebarrier).Thispreventsthecreationofmisleadinglookingdiagrams(sincethelinkisstillconsideredtobeconnectedtothenode).Ifyoudragthenon-arrowendofalinktoofarfromitsparentnode,thenthelinkwillbecome“disconnected”fromthatnode.Youcantellthishashappenedbecausethenameofthelinkwillsuddenlyappearattheendpointyouhavemoved(MoreInfo).

AutoGrid:IftheAutoGridison(thereisacheck-markinfrontoftheLayout→AutoGridmenuentry)thentheendpointsandbendsofalinkwillalwaysbeplacedongridpositionsafteramove.Thismakesiteasytoquicklydrawnetdiagramswithalignedlinksegments,andtomakesomesegmentsperfectlyhorizontalorperfectlyvertical.YoucanturntheAutoGridonoroffby=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">togglingLayout→AutoGrid,andsetthespacingofthegridwithLayout→GridSpacing.

NudgingBendsandEnds:Ifyouhavejustbeenmovingalinkbendorendpoint,andthelinkisstillselected,youcannudgethatbendorendpointalittletogetitexactlywhereyouwantbypressingtheappropriatearrowkey.Witheverypressofthekey,itwillmoveadistanceofthegridspacing,iftheAutoGridison,ortheminimumperceptibledistanceiftheAutoGridisoff.

SavingaNettoFileTosavethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenettoafile,chooseFile→SaveAsorclickthe toolbarbutton.Youwillbepromptedforthefilenameandwhatdirectorytoplaceitin.Afteryouhavesavedanet,itswindowtitlewillnolongerbe“Untitled-x”,butinsteaditwillbebasedonthenameofthefile.ThenyoucansaveitsubsequenttimesbychoosingFile→SaveorpressingCTRL+Swithoutbeingpromptedforthename.

Changed-Indicator:Ifthereisa*or+afterthetitleofthenetinitswindowtitlebar,thenitmeansthatthenethasbeenchangedsinceitwaslastreadorsaved,sothatthescreenversionisdifferentfromthefileversion.IfyouexitNeticaorclosethewindow,youwillbeaskedifyouwanttosavethechangesfirst.Whenyousavethenet,thechanged-indicatorwilldisappear.A*indicatormeanssubstantialchangeshavebeenmade,a+meansonlycosmeticchangeswere.(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_changed_indicator.htm');returnfalse;">MoreInfo)

FileFormat:ThenetnormallygetssavedasanefficientbinaryfileintheNETAformat(optionallyencrypted),withfileextension.neta.Thisfileismachineandplatformindependent,soNeticaApplicationandNeticaAPIonWindows,Linux,MacOS,Solaris,etc.usingIntel,AMD,PowerPC,ARM,etc.processorscanworkwithit.AllfutureversionsofNeticawillbeabletoopenit,andmostpastversionscanaswell(butofcoursebyignoringthenewNeticafeaturesthattheylack).

Fromthedialogboxforsavingthefile,youcanchooseanalternativeformatknownastheDNETformat(fileextension.dneor.dnet),fromthe"Saveastype:"choiceatthebottom.Itcontainsonly=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_ASCII.htm');returnfalse;">ASCIItext,soitisusefulifyouwanttoexamineoreditthefilewitha=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditor,orifitwillbereadbyotherprogramsthatunderstandDNET.AllfutureversionsofNeticawillbeabletoreadandwriteDNETfiles,andDNETfileshavethesameinteroperabilitydescribedaboveforNETAfiles.AdocumentpreciselydescribingtheDNET-1fileformatisavailablefromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsyswebsite(called“DNET_File_Format.txt”).

Cases:Tolearnaboutsavingandreadingcases,clickhere.

DeletingNodesandLinksNodes:Todeleteanodeornodes,firstselectthem,andthenpresstheDELETEkey,clickthe toolbarbutton,orchooseEdit→Delete.Alternately,youcanjust=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickanodeandchooseDelete.Thiswillremovethenodes,andalllinksfromothernodesgoingtothem.Linksgoingfromthemtotheirchildnodeswillbedisconnectedjustbeforethedeletion.Thesedisconnectedlinkswillbeselectedafterthenodesareremoved,soyoucaneasilydeletethemaswellbyjustpressingtheDELETEkeyasecondtime.

Ifyouwishtoremovethenodes,butmaintaintheglobalrelationshipoftheremainingnodes(i.e.thefull=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_joint_distribution.htm');returnfalse;">jointprobabilitydistribution),youshould=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_absorb_node.htm');returnfalse;">absorbthenodes.

Links:Todeletea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">link,clickonittoselectit,andthenpresstheDELETEkeyorchooseEdit→Delete.Todeleteaseriesoflinks,selectthemallandthenpresstheDELETEkey.Whenalinkisdeleted,theconditionalprobabilitiesofthechildnodearecollapsedtoeliminatetheirdependenceonthatparent,asiftheparenttookonitsfirststate.Whenalinkisdeletedtheparentnodeisnotaffectedinanyway.

Cut,Copy,PasteandDuplicateNodesCuttingNodes:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">Selectednodescanberemovedfromthenetandtransferredtothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboardbychoosingEdit→Cut(orpressingCTRL+X,clicking ,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingandchoosingDelete).

Alternately,theycanbeenteredintotheclipboardwithoutremovingthemfromthenetwithEdit→Copy(orpressingCTRL+C,orclicking ).

Ifnonodesareselectedwhenthecopycommandisdone,thewholenetwillbecopiedtotheclipboard.

PastingNodes:Oncethenodesareintheclipboard,youcanduplicatethemintoanynetbyopeningthewindowforthatnet,optionallyclickinginitwhereyouwantthemtobeplaced,andthenchoosingEdit→Paste(orpressingCTRL+V,orclicking ).Whencopyingfromonenetwindowtoanother,thetwowindowsmustbothbewithinthesamerunninginstanceofNetica;iftherearetwoseparateinstancesofNeticarunning,youcan'tcopyandpastebetweenthem.

Alllinksbetweenthetransferrednodes,alltheirproperties,andalltheir=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTswillbemaintainedduringthetransfers.Linksthatentercutorcopiednodesfromanodenotbeingcutorcopiedwillappearasdisconnectedlinksintheduplicate.Linksthatgofromacutorcopiednodetoanodenotbeingcutorcopied,willnotbecopied.

Netsmaybecopiedandpastedintootherprograms,suchasMicrosoftWord.

MoreInfo

Duplicate:Ifyouwanttoduplicatealargeportionofthenodes,chooseWindow→DuplicateNet(orright-clickthenetbackgroundandchooseDuplicateinNewWindow).Intheresultantnet,deleteanyofthenodesyoudon'twant.

NodeNames:Sinceeverynodenameinanetmustbeunique,anode’snamemustbechangedwhenduplicatingitintoanetalreadyhavingthatname.Neticadoesthisifnecessary,byaddinganumbertotheendoftheoldname,orincrementingthenumberiftherealreadyisone.Ofcoursenodetitlesdon’thavetobeunique,soafterduplicatingorpastingyoumayhaveseveralnodeswiththesametitle,whichyoucanchangemanually.

Right-ClickingYoucan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonnodes,linksandthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">background.Right-clickingonthebackgroundisforoperationsthatapplytothenetingeneral.Inallcases,amenuwillappearfromwhichyoucanchooseanoperation.IfyouareusingaMac,readthisFAQpagetofindaright-clickingalternative.

MenuContents:Thecontentsofthemenuswhichappearmayvaryfromtime-to-timedependingonthestatusoftheobjectbeingclickedon,andwhatotherobjectsareselected.Forinstance,theAlignitemappearsonlyifatleast2nodesareselected,andSpaceEvenlyonlyif3ormorenodesareselected.Thechoicesforaddinglinksdependonwhetherornotanynodesareselected,andwhetherornotyouclickonaselectednode(youshouldtrythethreepossibilitiestoseethedifferentwaysyoucanaddlinks).Ifyoudon'tseesomethingthatisusuallythere,trytheoverheadmenu.

Selection:Ifyouwantanoperationtoapplytoseveralnodesorlinksatonce,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthem,andthenright-clickononeoftheselectedones.Evenifsomeareselected,ifyouright-clickononethatisn'tselected,theoperationwillapplytothatoneonly.However,thereareafewmenuentriesthatalwaysapplyonlytotheelementbeingclickedon,evenifitispartofaselectedset.Theyare:Properties,SelectandDeselect(whichallowyoutoeasilyaddorremoveelementsfromtheselectedset).Moreinfoondoingoperationsonmultiplenodesatonce.

User-DefinedFields:Right-clickingprovidesagreatwaytoexamineorsettheuser-definedfieldsofanodeoranet,insteadofusingthenodepropertiesdialogbox.Right-clickonthenodeornetbackground,chooseModify→UserDefined,andamenuwillappearlistingallthefieldsforthatnodeand

theirvaluesin"field=value"form.Bychoosingoneoftheitems,youcanchangeit.Youcanevensetthefieldsforseveralnodesatonce.

Network:Ingeneral,theright-clickingmenushavethesamefunctionsastheoverheadones,buttherearesomedifferences,describedinthesectionsonaddingnodes,addingtitles/text,duplicatingthenetandselectingnodes/links.Youcanalsouseright-clickingtochangetheinternalnameofyournetbyright-clickingonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchoosingModify→Rename.Youwillberequestedtoenteran=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDnamethatwillbestoredwiththenetandusedtoidentifyitby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPI(thisisdifferentfromthenameinthetitlebar,whichisbasedonthefilenamethenetissavedto,althoughiftheinternalnameisnotset,itwillalsobebasedonthefilename).ThechoicesinthemenuModify→DefaultNodeStylesetthedefaultnodestylesforthenet(thesameastheoverheadStylemenuwhennonodesareselected).

PlacingTextonNetDiagramsYoucanputtextdirectlyonthenetdiagram,whichissuitablefortitles,comments,notes,copyrightandotherlegalnotices,small=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofnodes,warnings,directionsforusage,etc.

HowTo:Toaddatitleortexttoyournet,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchooseModify→NewTitleorNewNote.Aconstantnodewillbecreated.

Don'tUse:Ifyouhavealargeblockoftexttodocumentanet,itisbettertoplaceitinthedocumentationwindow,andifyouwanttoprovideadescriptionforanode,butnothaveitvisibleonthenetdiagram,usethenode’sdescriptionfield,orputitinastatecomment.

Color:Bydefault,textelementshavealight-bluebackground.Youcanmodifythisforthewholenetbyright-clickingonthenetbackgroundandchoosingModify→NodeSetProperties.Inthepropertiesdialogbox,clickon‘Documentation’andthenSetColor.Textelementscanbeaddedtonode-sets,soifyouwishtolinkthecoloringofatextelementtothatofsomenodes,addittothesamenode-settheyarein.Tomaketextelementsofvaryingcolor,createnewnode-setshavingthedesiredcolors.

FontandSize:Youcanalso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectsometextelements,andchangetheirfontorsizebyright-clickingonone,andchoosingStyle→Font.Itisnotpossibletohavemorethanonecoloringorfontwithinasingletextelement.

Youcanselect,search,copyandpaste,duplicate,edit,moveanddeletetextelementsinthenaturalway.Forexample,toduplicateanelement,youholddownCTRLkeyanddragit.Tochangethetextinit,youdouble-clickit.

Tips:

•Ifyouhavesometextelementsthatyouuserepeatedly,suchasacopyrightnotice,youcancopyandpastethemtotheNodePalette,foundontheWindowsmenu,sothattheywillbeavailableanytimeyouuseNetica.

•Thereareanumberofstyleoptionsavailableforimprovingtheoveralllookofyournet,whichisusefulforprintingandpresentationpurposes.

DocumentationWindowWhenyoucreateaBayesnetordecisionnet,itisusuallyagoodideatowriteashortdescriptionofit,orprovideotherwrittendocumentation,whichstaysinthesamefileasthenetitself.

Withthenetwindow=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">active,chooseWindow→DescriptionofNet,andawindowwillappearinwhichyoucanplace=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">plaintext.

Thisiscalledthenet’sdocumentationwindow,anditwillautomaticallybeclosedwhenthenetwindowisclosed.Ifthedocumentationwindowwasopenwhenthenetwaslastsaved,thenwhenthenetisnextopened,itwillautomaticallybeopenedaswell,andinthesameplaceaswhenthenetwassaved.

Tips:

•Ifyouaredistributingthenettootherpeople,makesurethedocumentationwindowisopenwhenyoulastsavethenet,sothattheyseeitrightawaywhentheyopenyournet.

•Informativetextcanalsobeplaceddirectlyonthenetdiagram,orwithinanode’sdescriptionbox.

NavigationandResizingUsingthescrollbarsyoucanmovearoundtovieworworkonvariousareasofthenet.TheHOME,END,PAGEUPandPAGEDOWNkeysandarrowkeysmaybeusedaswell.Whileyouaremovinganodeoralinkbend,youcanmakethewindowscrollbyattemptingtodragthemoutsidethewindowinthedirectionyouwishtoscroll.Thefurtheryougooutside,thefasteritscrolls.

ThefastestandmostpopularwaytonavigatetoanewspotistouseGlobalZoom.

SometimestheeasiestwaytoscrolltoanodethatyouknowthenameofistouseFind.Andyoucanjumptotheendofalinkby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingitandchoosingFindParentorFindChild.

YoucanalsoscrollbyholdingtheALTkeydownandclickingonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">background.Thecursorturnsintoahand,indicatingthatholdingthemousebuttondownanddraggingthemousewill"push"thenetdiagraminthatdirection.

GoBack:TohaveNeticaautomaticallyscrolltotheplacewhereyouwerepreviouslyediting(orclickedthemousebutton),chooseEdit→GoBack,orpressCTRL+SHIFT+G.Pressingitagainwilltakeyoutotheplacebeforethat,andsoon.Eventuallyyouwillreturntothestartingposition,soyoucanquicklycyclethroughthelast6placesvisitedbyrapidlypressingthekey.

DrawingSize:Theareawithinwhichyoucancreateanetdiagramisarectangleofcertainsize.Onceyouscrolltotheendofityoucannotscrollanyfurther.Thisareaisincreasedautomaticallywhenneeded,suchaswhendraggingorpastingnodespastitsboundary,orenlargingthewindow(includingmaximizingorzooming)biggerthanitssize.

YoucanalsomanuallychangethesizeofthisareabychoosingLayout→DrawingSize.Enteringblanksinthedialogboxthatcomesupwillmakethesizeassmallaspossibletocontaineverything.Thedrawingsizeisenteredas

thenumberofpageswidebythenumberofpagestall.Thesizeofapageisbasedonhowmuchyourprinterputsononeprintedpage,soitisinfluencedbyFile→PrinterSetup(seePrinting).

ZoomingInandOutWhenanetdiagrambecomeslarge,itishandytobeableto“zoomout”toseemoreofitinthewindowatonce.PressCTRL+>orchooseWindow→Zoom→Out.Eachtimeyoudothis,themagnificationofthedrawingwillbedecreased,soyouwillbeabletoseemoreofit.Toincreasethemagnification,pressCTRL+<orchooseWindow→Zoom→In.YoucanalsoaccesstheZoommenubyright-clickingonthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">background.

Whateverthezoommagnification,youcaneditorusethenetinthenormalway.

GlobalZoom:Neticaprovidesaveryfastandconvenientwayofobtaininganoverviewofadiagram,andquicklynavigatingtoanewpointonit,calledGlobalZoom.Whenalargenetdiagramisthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activewindow,youcanpresstheSPACEBARandholditdown.Whileitisdepressed,Neticawillzoomout,sothatthewholenetfitsinthewindow.Movethecursortothepointonthenetyouwishtoworkonnext,andthenreleasethespacebar.Neticawillzoombacktonormal,withthespotofinterestinthecenterofthescreen.

IfyouwishtouseGlobalZoomjusttogetanoverviewofthenet,butyoudon’twanttonavigatetoanewspot,thendon'tmovethemousecursoratall,orelsemoveitclearoutofthewindow,beforereleasingtheSPACEBAR.

ParticularMagnifications:YoucanzoomoutjustenoughthatthewholenetwillbedisplayedinthewindowbychoosingWindow→Zoom→ToFit.Afteranysequenceofzoomoperationsyoucanreturnto100%magnificationwithWindow→Zoom→ToNormal.

Window→Zoom→To...allowsyoutochooseanexactmagnificationamount,andWindow→Zoom→Backreturnsthemagnificationtowhatitwasbeforethelastzoomoperation.

Printing:Thezoommagnificationdoesnoteffectoutputsenttoaprinter;tochangethatmagnification,chooseFile→PrinterSetupandputblankentriesforthenumberofhorizontalandverticalpagesinthedialogboxesthatcomeupafterwards.Youwillthenbequeriedforaprintermagnification.

Tip:Oftennetsarebuiltusingalargerfont,thenasthenetsgetbigger,developersjustzoomoutabitandcontinuebuilding.Insteadbuildthenetusingaslightlysmallerfontsize,andworkatNormal(100%)zoommagnification,sinceNeticaisoptimizedforthat.

Search/FindTofindtheoccurrenceofsometextinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenet,chooseEdit→Findandenterthesearchtext.Neticawillsearchnodenames,titles,statenamesandcommentsforthetext.

WhenNeticafindsanodecontainingthesearchtextitwillscrollthewindowtothatnodeandselectthenode.Tofindthenextnodecontainingthetext,useEdit→FindNext(orpresstheF3key).Edit→FindAllwillselectallthenodescontainingthetext.

Youmayonlybeinterestedintheoccurrenceofthesearchtextinonetypeoffield;sayyouarelookingforthenodewithacertainname.AsNeticafindseachoccurrenceofthesearchtext,itprintsinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowwhereitfoundthetext.Forexample,itmightprint:"heavypressure"foundincommentofnodeDepth.SoyoucanjustwatchtheMessageswindowuntilyouseethatNeticafoundthetextinanodename.

Tips:

•Ifyouwanttoeasilyselectacertainsubsetofnodes,youcangivethemakeyword,say"$Unfinished",byputtingthatkeywordinthedescriptionofeachofthem.WheneveryouwanttoselectthemjustdoanEdit→Findon"$Unfinished",andthendoEdit→FindAll.Itisgoodtoprecedekeywordswithsomespecialsymbol,like‘$’,sothesearchcan’tbeconfusedbynodetitles,statenames,etc.,andyouwillrememberitisbeingusedasakeyword.However,usuallyabettermethodtoworkwithsetsofnodesistonode-setsandselectthembasedontheirnode-setnames.

•Youcanmakeaprintedlistofallthenodescontainingcertaintext,byfirstdoingaFindAllsearchonthattext,thenwiththenodesstillselected,

chooseReport→ListofSelected.MoreInfo

SelectingNodes/LinksbyPropertiesInadditiontothewaysformanuallyselectingnodesorlinks,youcanmakeselectionsbasedonthepropertiesorrelationshipsofnodesorlinks.

BychoosingEdit→SelectNodesfromtheoverheadmenu,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchoosingSelectNodes,youwillbepresentedwithalistofthefollowingoptions:

SelectNodes→All-Allthenodesincludingconstantnodes,andalsotitlesandnotes.

InvertSelection-Nodesthatarecurrentlyunselected(andde-selectsthosethatareselected).

InNodeSet-Thenodesthataremembersofthechosennode-set.

ListedinClipboard-Thosenodeswhosename(nottitle)appearspreciselyinthetextyouhavejustcopiedtothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboard(multiplenodesshouldbeseparatedbycommasor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_whitespace.htm');returnfalse;">whitespaces).

MatchSearchString-Allnodeswhosename,titleorstatenameortitle,ornodedescriptioncontainsthesearchtext(whichyouwillbeaskedfor).

WithTables-Anynodeswhose=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTtableor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontableiscompletelyfilledin.

IncompleteTables-AnynodeswhoseCPTtableorfunctiontableisnotcompletelyfilledin(i.e.,containssomeblankentries).

WithEquations-Nodesthathavean=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equationdefined.

WithFindings-Nodeswithanytypeoffinding("evidence"),includingpositive,negativeorlikelihood("virtual")findings.

LikelihoodFindings-Nodeswithonlya=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">likelihoodfinding("virtualevidence"),ormultiplelikelihoodfindingsthataren'tequivalenttoasingle=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefinding.

Parents-Allnodesthathavealinkpointingtosomecurrentlyselectednode.

Ancestors-Allnodesthathaveapathofforward-pointinglinkstosomecurrentlyselectednode.

Children-Allnodesthathavealinkcomingfromsomecurrentlyselectednode.

Descendents-Allnodesthathaveapathofforward-pointinglinksfromsomecurrentlyselectednode.

Connected-Nodesthathaveapathoflinks(ignoringdirections)tosomecurrentlyselectednode.

Info(D-)Connected-Thenodeswhosebeliefscouldchangeifafindingwereobtainedforacurrentlyselectednode,basedonthegraphconnectivity(orvice-versa).Thesearethenodesthatarenot=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_d_separation.htm');returnfalse;">d-separatedwiththecurrentselection.YoucoulduseInvertSelectionafterthisoperationtofindthenodesthatared-separated.

MarkovBoundary-Nodesinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Markov_boundary.htm');returnfalse;">Markovboundaryofcurrentlyselectednodes.If=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefindingsareobtainedfortheMarkovboundarynodes,thenthevaluesofthecurrentlyselectednodeswillnotprovideanyadditionalinformationaboutanyothernodeinthenet.

SelectLinks→All-Allthelinksinthenet.

Disconnected-Allthelinksinthenetwhichhavebeen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_disconnected_link.htm');returnfalse;">disconnectedfromtheirparents.

Ineffectual-Allthelinksinthenetwhichhavenoinfluenceonanyinferenceresults,becausetheyare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_ineffectual_link.htm');returnfalse;">ineffectual.

Entering-Alllinksdirectlyenteringanodewhichiscurrentlyselected(i.e.hasaselectednodeasachild).

Exiting-Alllinksdirectlyexitinganodewhichiscurrentlyselected(i.e.hasaselectednodeasaparent).

Interconnecting-Thelinkswhichdirectlyinter-connectthecurrentlyselectednodes(i.e.havebothachildandaparentwhichisselected).

Cyclecontaining-Ifthereisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_cycle.htm');returnfalse;">directedcycleinthenet,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingwillbedisallowed,andthishelpstofindit.Selectalinkinthecycle(perhapsasreportedbyanerrormessage),andusethisoperationtoselecttherestofthecycle.

OneOperation,MultipleNodesNormallyyoumodifyanodeusingthenodepropertiesdialogbox,whichallowsyoutochangeanyofthepropertiesofasinglenode.However,sometimesyouwanttomakethesamechangetoseveralnodesatonce.WithNetica,youcanadd,remove,renameorreorderstates,changediscretizationthresholds,enterfindings,enteruser-definedfields,changenode-sets,etc.toasmanynodesaswish,withoneoperation.

HowTo:Selectthedesirednodes,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickononeofthem,andmakeachoicefromthemenu.Anychoiceyoumakewillapplytoallthenodes,exceptforthechoices:Select,DeselectandProperties.

EnteringFindings:Whenseveralnodesareselectedandyouright-clickononeandchooseEnterFindings,youwillbepresentedwithamenuthatlistsallthestatesofallthenodesselected,withanyfindingsalreadyenteredhavingcheck-marks.Ifyouchooseastatefromthelist,theneverynodehavingthatstatewillgetitenteredasafinding,whiletheotherselectednodeswillnothavetheirfindingchanged.Ifyouwanttheotherfindingsremoved,thenyoushouldfirstchooseEnterFinding→Unknown(Retract),andthenthedesiredfinding.Iftheselectednodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousnodes,thenyoucanenteranumericfindingforthemallsimultaneouslyusingEnterFinding→NumericValue.

SettingStates:Thereare4choicesforchangingthestatesofanodeavailablefromtheModifymenu:AddState,DeleteState,RenameStateandSetStates.Thefirst3arefairlystraightforward;theyadjustalleffected=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTstoproducetheleastdisturbancepossible.InthecaseofAddStateandRenamestate=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">inferenceresultswillnotbeeffectedatall.SetStateshasthemorecomplexbehaviour:

•Ifthenewstateshaveexactlythesamenamesastheoldones,andthereisthesamenumberofthem,butjustinadifferentorder,itre-ordersthestatesandallrelatedstructures(suchas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">staterealvaluesandCPTs),sothatallinferenceresultswillbeunaffected.•Otherwise,iftherearethesamenumberofstates,itjustrenamesthestates(soinferenceresultswillbeunaffected).Warning:Ifthereareadifferentnumberofstates,allrelatedstructures(suchas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">staterealvalues,statetitlesandCPTs)areremoved,whichofcoursewilleffectinferenceresults.Ifyouwanttokeepthetables,thenyouneedtouseModify→AddStateorModify→DeleteStateinstead.

User-DefinedFields:Asdescribedontheright-clickingpage,youcansetuserfieldsofanodebyright-clickingandchoosingModify→UserDefined.Ifyouclickononeofseveralselectednodes,thenamenuwillappearlistingallthefieldsalreadydefinedforatleastoneoftheselectednodes.Bychoosingafield,youcansetitsvalue.Ifthefieldwasoriginallydefinedforonlysomeofthenodes,Neticawillaskyouifyouwanttochangethevalueofonlythosenodes,orwhetheryouwanttoaddthefieldtoallthenodes.Ifyoumakeafieldempty,Neticawillaskyouwhetheryouwantittorepresentanemptyfield,orifyouwantthefieldremoved,whichyoucanusetoremovefieldsfromalargesetofnodesatonce.Likewise,youcanaddafieldtoalargenumberofnodesbychoosingModify→UserDefined→Enter,andthenenteringthenameofthenewfield.

NodePropertiesThischapterexplainshowtousethenodedialogboxtovieworchangethepropertiesofanode.Youcanpagethroughtheentirechapterusingthe>>buttonabove,seeawrittendescriptionofwhereinformationis,orjumpdirectlytooneofthefollowingtopics:

•NodeDialogBox•ButtonsintheNodeDialogBox•NodeName•NodeTitle•NodeisDiscreteorContinuous•NodeKind•NodeStates•NodeStateInterval•NodeStateValue•User-DefinedFields

NodeDialogBoxPurpose:Youusethenodedialogboxtochangethepropertiesofanode(e.g.itsname,orhowmany=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">statesithas).Tochangethewayanodeisrelatedtoitsparents(e.g.,itsconditionalprobabilities),usethetabledialogboxinstead,andtochangethecolorofanode,seeNodeColoring.

Obtaining:Double-clickanodetoobtainitsnodedialogbox,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonitandchooseProperties,orselectitandpresstheENTERkey.Thelattermethodisveryusefulwhenaddingnewnodestoanet,sincewhenanodehasjustbeenaddeditisalreadyselected,andyoujustneedtopressENTER.

Thenodedialogboxcanbeusedtosetanode's:•Name •Statenumbers

•Title •Stateintervals(discretization)

•States •User-definedfields

OtherFields:Atthebottomofthenodedialogboxisatexteditingbox,calledthemultipurposebox,withinwhichyoucanvieworchangesomeothernodeproperties,aschosenbythe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_multipurpose_selector.htm');return

false;">multipurposeselector.

Buttons:Bypressingthe selector,youcanchoosethenodekindfromtheoptionslisted.Ifyouclickthe selector,youcanchangethenodefromdiscretetocontinuous.MakingachangewithinthedialogboxdoesnotaffectthenodeuntiltheApplyorOkaybuttonispressed(moreinfoontheright-handbuttons).

Multiple:Youmayhaveseveralnodedialogboxesonthescreenatthesametime,andyoumayalternatebetweenusingdifferentnodedialogboxesandworkingdirectlyinthenetwindow.Eachnodedialogboxpertainstoasingleparticularnode,butyoucanhavemorethanoneofthemforthesamenode.

ButtonsintheNodeDialogBoxApply&Okay:Whenyoumakechangesinthenodedialogbox,theydon’taffectthenodeuntilyouclicktheApplyorOkaybutton.Thenallthesettingsaretransferredtothenodeinthenet.TheApplyandtheOkaybuttonshavethesamefunction,excepttheOkaybuttonalsoremovesthedialogboxaftertransferringthesettings.

Reset:ClickingtheResetbuttonwillmakeallthesettingsinthedialogboxthesameasthenodeinthenet.Ifsomeexternaloperationchangesthenodeinthenet,thesettingsinthedialogboxaren'tchangedtoreflectthatuntiltheResetbuttonispressed.

Close:IfyouclicktheClosebuttonorthe buttoninthetitlebar,thenodedialogboxwillberemoved.Ifyoupreviouslymadesomechangesinit,andhaven’tpressedtheApplybutton,Neticawillaskifyouwanttoapplythosechangesfirst.

Table:ClickingtheTablebuttonwillbringupthetabledialogboxforthesamenode,tovieworedititstables(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPT,experience,etc.).

Help:WhenyouclicktheHelpbutton,itwillbringuptheNodeDialogpageofthisHelpsystem.

NodeNameYoucanchangethenameofanodeusingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_node_name.htm');returnfalse;">“Name”texteditboxofthenode’sdialogbox.Whenthedialogboxfirstappears,theexistingnameofthenodeisselected,soifyoujusttypeanewnameitwillreplacetheexistingname.

Whenyouenteranewnodename,Neticawillcheckthatitmeetstherestrictionsofan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname.Ifyouwanttocircumventtheserestrictions,youcanalsogivethenodeatitle.

Note:Whenanode’snameischanged,Neticawillautomaticallyadjusttheequationofthenodeandtheequationsofallit’schildrennodes.

NodeTitleThenodedialogboxhasatexteditboxlabeled=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_node_title.htm');returnfalse;">“Title”toprovideanunrestrictedalternativetothenode’sname(whichmustbean=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname).Youcanchoosewhetherthename,titleorbothareusedtolabelanodeonnetdiagrams.

Therearenorestrictionsonwhatyoumayputinatitle,andbyusingtheENTERkeyyoucanmakethetitlemorethanonelinelong.Keepinmindthatsomeunusualcharactersmaydisplaydifferentlywhenthefontischanged,orifthenetisdisplayedonanothertypeofcomputer.Nodetitlesmaycontaincharactersfromanylanguage.

Nodesarenotrequiredtohavetitles.Ifanodedoesnothaveatitle,thenanytimethatNeticawouldnormallyuseatitle,itwillusethenode’snameinstead.Thetitleisonlyusedtolabelthenode;anythingmoredetailedshouldgointhedescriptionofthenode.

Tips:

•Ifthetitleislongerortallerthanthetextentrybox,youcanscrollitusingthearrowkeys.•=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">Right-clickwhileeditingatitletoobtainapop-upmenuforcopying,pasting,etc.•Byputtingablanklineatthebeginningorendofthetitle,orputtingaspacecharacteratthebeginningorendofatitleline,youcaneffectivelyaddsomespacebetweentheoutsideborderofanodeandthewritingwithin.

NodeisDiscreteorContinuousThenodedialogboxhasaselector: withthevaluesContinuousandDiscrete,whichallowsyoutochoosewhetherthenoderepresentsa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariable.

Itiscommontohaveacontinuousvariablethatyouwanttobreakupintointervalssothatyoucantreatitasadiscretevariable,whichisknownasdiscretizingthevariable.Ifthevariableistrulycontinuous,itisusuallybesttomakeitacontinuousnode,andthendiscretizeitwithanintervallist,ratherthanjustmakingita=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenode.Thisprovidesbetterdocumentationofthenode,andmakesiteasierifatalatertimeyouwanttodiscretizeitanotherway(i.e.withadifferentnumberofstates,ordifferentcutoffpointsforthestateintervals).Also,thatwayitcanacceptcontinuousvalueswhenlearningfromcases,orgeneratethemwhensimulatingcases.

Alternately,adiscretenodemayhavenumericquantitiesattachedtoeachstate,sothateachstatecanrepresentanumber,butthevariableisincapableofrepresentingnumbersbetweenthoseofeachstate.MoreInfo.

Note:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">Utilitynodesmustbecontinuousand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodesmustbediscrete.

NodeKindDirectlybelowthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_node_name.htm');returnfalse;">nameentryareaofthenodedialogboxisaselector .Clickonittobringupthenodekindsmenu:

.

Youcanuseittoturnthenodeintoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_Glossary_NR.htm#nature');returnfalse;">naturenode,constantnode,decisionnode,orutilitynode(alsoknownasa“valuenode”).

Naturenodesarecalleddeterministicnodeswhentheirrelationshipwiththeirparentsisdeterministic,orchancenodeswhentherelationshipisprobabilistic.Neticawillautomaticallydetermineifanaturenodeisdeterministicandifso,willdrawathickborderwheninlabeled-boxstyle,andcoloritinthe"-Deterministic"node-setcolor(ifyouhaven'tmadeothernode-setshigherpriority).

WhenanetiscomposedentirelyofnaturenodesitiscalledaBayesnet(alsoknownasa“beliefnetwork”).Ifitalsohasdecisionandutilitynodes,itiscalledadecisionnet(alsoknownasan“influencediagram”).=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">Decisionnodesrepresentvariablesthatthedecisionmakercancontrol,and=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynodesrepresentvariablesthedecisionmakeristryingtooptimize.

AlternativeWays:Youcanalsochangenodekindsstraightfromthenet

windowwithoutusinganodedialogbox.Todothis,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectanodeorsetofnodesyouwishtochange,andwhileholdingdowntheCTRLkeyclickthetoolbarbuttonindicatingthekindofnodeyouwishthemtobecome: fornaturenodes, fordecisionnodes,or forutilitynodes.

Or,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickoverthenode(orselectednodes)andchooseModify→Kind.

NodeStatesInthenodedialogbox,nexttothelabel=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_states.htm');returnfalse;">“State”,isadown-arrowwhichyieldsapop-upmenuofthenode’s=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">states.Bychoosingastatefromthemenu,itbecomesthecurrentstateofthenodedialogbox.Itsnamewillappearinthetexteditboxtotherightofthepop-upmenu,allowingyoutomodifyit.

Thestatesofanodeconstitutethedomainofacategoricalvariable.Theyarenotrequiredtohavenames,butifonestateisnamedthentheyallmustbe.Itishighlyrecommendedthata=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenodebegivenstatenames,forclarityanddocumentationpurposes,althoughitisnotnecessaryfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizedcontinuousnodes.

StateName:Whenyouenteranewstatename,Neticawillcheckthatitmeetstherestrictionsofan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname.Also,itmustbedifferentfromthenamesofallotherstatesofthatnode,althoughitmaybethesameasastatenameforadifferentnodeinthenet.Ifyouneedunrestrictedlabels,usestatetitles.

Adding/Removing:Toaddanewstaterightafterthecurrentstate,clicktheNewbutton,andtodeletethecurrentstate,clicktheDeletebutton.Alldiscretenodesmusthaveatleastonestate,butthereisnoupperlimittohowmanytheycanhave.AddingorremovingseveralstatestoanodeatonceisusuallydonemoreconvenientlybyusingtheMulti-PurposeBox,andadding

orremovingastatefromseveralnodesatonceisbestdonebyright-clicking.

MultipleNodes:Changingthestatesofanode,ormanynodesatonce,canbedonequicklyandeasilyby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonanode,oragroupof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectednodes,andchoosingModifytodooneofthefollowingoperations:AddState,DeleteState,RenameState,andSetStates(moreinfo).

Ifyouareaddingastatetomultiplenodes,andsomeofthemalreadyhaveastateofthatname,theywillsimplybeskipped.Iftheexistingstateshave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">numericvaluesdefined,andyouenteranumber,thenyouwillbegiventheoptionofaddingstateswiththatnumericvalue,orstatestitledwiththenumber.

Seealso:OrderingStates

OrderingStatesRight-clickonanode(orifyouwanttodoseveral,selectthemandthenright-clickononeofthem),thenchoosefromthemenuModify→OrderStates→ByName,ifyouwanttheminalphabeticalorder.

Ifyouwanttheminsomeotherorder,chooseModify→OrderStates→StandardOrder.Todefinewhatstandardorderis,editthetextfile"StateOrder.txt".ItislocatedinthesamedirectoryasNetica.exe,whichcanbediscoveredbychoosingHelp→AboutNetica,andthenlookingintheMessageswindow.Youcanuseanytexteditor,suchasNotePad,oryoucanchoosefromtheNeticamenuFile→OpenAsText.

Inthefile,thestatenamesortitlesappearone-per-line,intheorderyouwouldlikethemtohaveinthenode.Viewingtheexistingfilewillmakeitclear.

Ifyouwanttohaveadifferent"StateOrder.txt"fileforsomeparticularsetofBayesnets,thenyoucanputoneinthesamefolderasthoseBayesnets,andNeticawilllookforittherefirst.

Whenre-orderingthestates,Neticawillfirsttrytomatchthestatetitleagainsttheentryinthe"StateOrder"file,andifnotfound,thenthestatename.Ifsomeentriesinthe"StateOrder"filedifferonlybyupper/lowercaseofsomecharacters,Neticawillproperlyconsiderthecasewhileordering(i.e.casesensitive).Howeverifthereisnoexactmatchbycase,butthefilecontainsanentrythatisalllowercase,thenNeticawilldoacase-insensitivematch.Forthatreasonentriesinthe"StateOrder"fileoftenallappearinalllowercase.

Ifyouchangethe"StateOrder"file,youneedtore-openanyBayesnetsforwhichyouwereorderingstatesforthenewfiletotakeeffect.

NodeStateIntervalIfanodedialogboxisfora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousnode,immediatelybelowthestatenameeditboxwillbeboxeslabeled“Interval”.Thesearetoprovide=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_threshold.htm');returnfalse;">thresholdvaluesfortheintervalsofeachstateinorderto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizethecontinuousvariable.Thismethodofenteringthethresholdsismainlyjustfortouch-upwork,ortocoordinatetherangeswithstatenames,sinceusuallythresholdsareenteredusingtheMulti-PurposeBox.

Theboxtotheleftisthelowerendoftheintervalforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_current_state_node_dialog.htm');returnfalse;">currentstate(inclusive),andtheboxtotherightistheupperendoftheinterval(exclusive).

Tosetorchangetheintervalofthecurrentstatesimplytypeanumberintheappropriatebox.Statesarearrangedinacontiguousand(increasingordecreasing)monotonicway,whichmeansthattheupperendofonestateintervalwillalwaysbethelowerendofintervaloftheneighboringstate.Asyoutypeoneofthesein,Neticawillfillintheotheraswell,sothatwhenyouchangethecurrentstateyouwillseethenumberyoujustenteredinoneoftheIntervalboxes.

Itisokayifthelowerandupperboundsofanintervalarethesamenumber,toindicateapoint.Thenumbersyouentermaybeintegers,decimalnumbers,scientificnotationnumbers,“infinity”,or“-infinity”.

NodeStateValueIfanodedialogboxisfora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenode,immediatelybelowthestatenameeditboxwillbeaboxlabeled“Value”.Thisistoassociateanintegerorarealnumbervaluewitheachstate.Thatnumbercanbeanythingyouchoose,andshouldnotbeconfusedwiththestateindex,whichisanintegerstartingat0forthefirststate,andincreasingbyoneforeachsubsequentstate.

Usuallyyouwillnotneedtoassignnumberstostates,butsometimesitisuseful.Forexample,thenumbersmayrepresenthowmanyheadswereobtainedin4cointosses.Asanotherexample,inabang-bangcontrolsystem,state0(“Off”)maymapto-0.2volts,andstate1(“On”)maymapto6.0volts.Ifthisnodeistheparentofanodewithan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equation,thentherealvalueswillbesuppliedtotheequation.

Tosetorchangetherealnumberassociatedwiththe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_current_state_node_dialog.htm');returnfalse;">currentstatesimplytypeanumberinthebox.YoumayfinditeasiertousetheMulti-PurposeBoxtoenterorchangetherealnumberassociatedwithastate.Youcanalsochangethisnumberbyright-clickingonanunselecteddiscretenode(oraselectionofnodes)andchoosingModify→NumericStateValues.moreinfo

Tips:

•Tocreateanewnodewithnodestatevaluesalreadyassigned,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandthenchooseModify→NewNode→Nature-NumericDiscrete.Inthedialogboxthatcomesupyoucanuseshorthandnotationlike[5,10]+1.

•Ifthe"numbers"youareassigningasnodestatevalueshavenorealnumericsignificance(e.g.theyarejustidentifyingnumbers),thenyoumaywanttomakethemnodestatetitlesinstead,sothatNeticadoesn'ttrytointerpretthemasnumbers.

•IfyouneedtoadjustNeticanodestobeabletoreadacasefileinwhichacategoricalvariableisindicatedwithintegers(forexample,daysoftheweekbeing1to7,orgenderbeing1or2),youcanassigntheappropriateintegertoeachstateofthenodeasthestatevalue.

User-DefinedFieldsSometimesitisusefultobeabletodefineyourownfieldsfornodesornets,withnamesthatyouchoose,andgivethemthekindofvaluesyouwant(integers,realnumbers,ortext).Thesehavesometimesbeencalledattribute-valuepairs,andaresavedintheBayesnetfilealongwiththerestoftheinformationaboutthenodesandnet.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPIcanalsoreadandsetuser-definedfields,sotheyareagreatwaytocommunicatewithyourownprogramthroughNeticaApplicationandthenNeticaAPI.

Therearetwowaystoworkwithuser-definedfields.ThefirstisdescribedinapageontheNodePropertiesDialog.Thesecondisdescribedbelow.

Setting:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">Right-clickonanodeandchooseUserDefined→Entertocreateanewuserfield,orUserDefined→fieldnametochangethevalueofanexistingone.Ifyoucreateanewuserfield,Neticawillverifythatitsnamemeetstherequirementsofan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname.Youcandothesamethingtoseveralnodesatonceby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingthembeforeright-clickingoneofthem,andyoucandoittothenetitselfbyright-clickingonthenet's=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchoosingModify→UserDefined→fieldname.

Observing:Toobservethevaluesassignedtouserfieldsofanodeornet,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickthenodeornetbackgroundandchooseUserDefined.Thevalueswillappearwithinthemenu.Iftheyaretoolargeforthemenu,orcontainspecialcharacters,youcanusetheNodePropertiesDialoginstead.

Removing:Toremoveafieldfromanode,right-clickthenodeandchooseUserDefined→fieldname.Whenthedialogboxaskingforthevaluecomesup,makeitemptyandpressOkay.ThenNeticawillaskyouifyoujustwantanemptyvalue,orifyouwanttoremovethefield.Youcandothesamethingtoseveralnodesatoncebyselectingthembeforeright-clickingoneofthem,andyoucandoittothenetitselfbyright-clickingonthenet'sbackgroundandchoosingModify→UserDefined→fieldname.

Tips:

•Ifyouwanttodefinethesameuser-fieldforseveralnodesatonce,butgivethemeachdifferentvalues:Selectthenodes,right-clickandchooseUserDefined→Enter,enterthenameyouwantforthefieldandpressOkay,thenleavethevalueboxemptyandpressOkay,No.Nowgotoeachnodeandright-click,thenchooseUserDefined→fieldname.Youwillbeabletokeeptrackofwhichonesyou'vealreadyentered,basedonwhichareempty.

•Forcategorizingnodes,ratherthanuser-definedfields,youmaywanttousenode-sets,sinceNeticahassomespecializedfeaturesforworkingwiththem,suchas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingallthenodesinsomenode-set,reportingallthenodesinanode-set,andchoosingdisplaycolorsbasedonnode-sets.

•Iftherearesomanyuserfieldsthatitisdifficultchoosingthenamefromamenu,insteadofchoosingUserDefined→fieldname,youcanchooseUserDefined→Enter,andthentypethenameoftheuserfieldyouwanttoviewormodify.

Multi PurposeBoxAtthebottomofthenodedialogboxisatexteditboxwithaselectoraboveit(calledthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_multipurpose_selector.htm');returnfalse;">multi-purposeselector).Thisboxisusedtovieworenterseveraldifferentpropertiesofthenode,andtheselectoristochoosewhichpropertytovieworenter.Thechoicesare:

•Description•Equation•Thresholds(fordiscretization)•StateNumbers•States•StateTitles•StateComments•Input(link)Name•Delay•Author•WhenChanged•UserDefined

Toscrollinthetexteditbox,clickdownwithintheboxandthendragthecursorinthedirectionyouwishtoscroll,orusethearrowkeystoattempttomovetheinsertionbarpastthebox’sboundary.

Ifyouhavealargeamountoftexttoedit,youmightfinditeasiertocreateitinaregular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditor,andthencutandpasteitintothemulti-purposebox.

NodeDescription–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoDescription,youcanenterorviewthedescriptionofthenode.Thedescriptionisanunrestrictedblockofplaintextwhichcanbeusedtostorewhateverinformationaboutthenodeyouwish,suchasitsmeaning,themeaningsofitsstates,howitistobemeasured,theoriginofitsprobabilities,copyrightinformation,etc.Thedescriptioniscurrentlylimitedtoabout30thousandcharacters.

Descriptiveinformationaboutanodecanalsoappeardirectlyonthenetdiagram.Whereasdescriptiveinformationrelativetotheentirenetshouldappearinthedocumentationwindow.

Inaddition,youcaninsertacommentthatwillcomeupdirectlyintheBayesnetwheneveryourestthecursoroveraspecificnode.Todothis,intheDescriptionfield,enclosethedesiredcaptionwithsquarebracketsandstars,forexample:

[*desiredcaptiontobedisplayed*]

NodeEquation–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoEquation,youcanvieworentertheprobabilisticordeterministicequationthatprovidestherelationbetweenthenodeanditsparents.

Formoreinformationonequations,see:UsingEquations,EquationSyntaxorBuilt-InFunctions

NodeDiscretization–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoDiscretization,youcanenterorviewthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizationthresholdsofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousvariable(ifthevariableis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretethenthemenuwon'thavea"Discretization"choice).YoucanalsodothisoperationusingtheIntervalsettingboxes,whichhavethesamecapabilitiesandeffect.However,usuallythebelowmethodismoreconvenient,especiallyifyouwanttoentermanyevenlyspacedvalues,orifyouwanttopasteinthethresholdsofallthestatesatonce,whichyouhavecopiedfromanothernodeorevenfromanotherprogram.

Yousimplyenteralltheintervalthresholdsintothebox,separatedbyspace(s),tabs,commasoronseparatelines.Thereshouldbeonemorenumberthanthedesirednumberofstates,sincethefirstandlastnumberspecifytheminimumandmaximumvaluesthevariablecantake(theycanbe"infinity"or"-infinity"ifdesired).Ifthenumberofstatesimpliedbythelistisdifferentfromthenode’scurrentnumberofstates,thenode’snumberofstateswillbechanged.

ShortcutNotation:Ifyouwanttocreatealistofevenlyspacedvaluesthereareafewshortcutmethodsyoucanuse.Eachofthefollowingspecialnotationswillexpandintoalistofnumbersasdescribed:

[b,e]/nwillformalistbeginningwithb,endingwithe,andhavingnintervals(son+1numbers).

[b,e]+dwillformalistbeginningwithb,endingwithe,andeachseparatedbyd(exceptthelastseparationmaybelessife–bisnotevenlydivisiblebyd).

[b,e]/Lnwillformalistbeginningwithb,endingwithe,anddividedlogarithmicallyintonintervals(son+1numbers).

[b,e]+%dwillformalistbeginningwithb,endingwithe,andeachbeingdpercentbiggerthantheprevious(exceptthelastmaybelessthand%bigger,iftheydon’tfitevenly).

Note:Ifeislessthanbthenadecreasinglistwillbeformed,butnanddshouldstillbeenteredaspositivenumbers.Theclosingbracketmaybereplacedwithaclosingparenthesisifdesired,toindicateexcludingtheendpointefromthelistformed.Morethanoneoftheabovenotationscanbecombinedtoformalongerlist.

Examples:Eachlinebelowisacompleteexampleentry:

-3.2011e4infinity

[0,10]/10

[0,10)+1,[10,20)+2,[20,30)+3,33,37

[1e6,1]/L6

[200,10]+%15

NodeStates–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoStates,youcanenterorviewhowmanystatesthenodehas,andwhattheirnamesare.YoucanalsodotheseoperationsusingtheStateNamesettingbox,whichhasthesamecapabilitiesandeffect.However,usuallyyouwillfindthismethodmoreconvenient,especiallyifyouwanttopasteinthenamesofallthestatesatonce,whichyouhavecopiedfromanothernodeorevenfromanotherprogram.

Yousimplyenterthenamesofallthestatesintothebox,separatedbyspace(s),tabs,commasoronseparatelines.Ifthenumberofstatesinthelistisdifferentfromthenode’scurrentnumberofstates,thenode’snumberofstateswillbechanged.

Anexampleentryis:lowmediumhigh

Thisoperationcanalsobeperformedbyusingtheright-clickmenu.YoucanRenameorDeleteStatesbyright-clickingonasingleorgroupofnodesandchoosingModify.Adialogboxwillcomeupaskingwhichstateyouwanttorenameordelete.MoreInfo

NodeStateNumbers–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoStateNumbers,youcanassignanumbertoeachstateofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariable,orviewthecurrentassignments(ifthevariableis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousthenthemenuwon'thavea"StateNumbers"choice).YoucanalsodothisoperationusingtheStateValuesettingbox,whichhasthesamecapabilitiesandeffect.However,themulti-purposeboxisusuallymoreconvenient,especiallyifyouwanttoentermanyevenlyspacedvalues,orifyouwanttopasteinthenumbersofallthestatesatonce,whichyouhavecopiedfromanothernodeorevenfromanotherprogram.(moreinfoonstatenumbers)

Yousimplyenterallthenumbersintothebox,separatedbyspace(s),tabs,commasoronseparatelines.Thereshouldbeonenumberforeachdesiredstate.Ifthenumberofstatesimpliedbythelistisdifferentfromthenode’scurrentnumberofstates,thenode’snumberofstateswillbechanged.

ShortcutNotation:Ifyouwanttoquicklycreatealistofevenlyspacedvalues,youcanusethesameshorthandnotationasusedfordiscretizinganode.

StateTitles–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoStateTitles,youcanenterorviewthetitleofeachnode.

Therearenorestrictionsonwhatyoumayputinatitle,andbyusingtheENTERkeyyoucanmakethetitlemorethanonelinelong.Keepinmindthatsomeunusualcharactersmaydisplaydifferentlywhenthefontischanged,orifthenetisdisplayedonanothertypeofcomputer.

Statesarenotrequiredtohavetitles.Ifastatedoesnothaveatitle,thenanytimethatNeticawouldnormallyuseatitle,itwillusethestate’snameinstead.Thetitleisonlyusedtolabelthestate;anythingmoredetailedshouldgointhestatecommentsofthenode.

StateComments–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoStateComment,youcanenterorviewcommentsspecifictoeachstateofthenode.Foreachstatelisted,youcanenterspecificcommentsaboutwhatthatstatemeans,orthepurposebehindhavingthestate.Therearenorestrictionsonwhatyoumayputinacomment.

Inaddition,youcaninsertacommentthatwillcomeupwithintheBayesnetwhenyourestthecursoroveraspecificstate.Todothis,inthestatecommentfield,enclosethedesiredcommentwithsquarebracketsandstars,forexample:

[*desiredcommenttobedisplayed*]

InputName–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoInputName,youcanvieworenteranameforeachofthelinksgoingtothenode.AssoonasyousettheselectortoInputName,anadditionalselectorwillappeartotherightofit.Eachchoiceofthenewselectorwillcorrespondtoalink,andwillbelabeledwiththecurrentlinknameifthelinkhasone(inparenthesis),and/orthenameoftheparentnodeitcomesfromifthelinkisnotdisconnected.

Makeachoicefromtheright-handselector,andthenentertheinput-nameintheboxbelow(itmustbealegal=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname).

Inputnamesareusedfornetlibrariesandequations.

Theinputnamewillappearonthenetdiagramwhenyouhoverthecursoroveritslink.

Note:YoucanalsosetInputNamesby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingalink(s)andchoosingInputName.

LinkDelay–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoLinkDelay,youcanvieworenteratime-delayforeachofthelinksgoingtothenode.AssoonasyousettheselectortoLinkDelay,anadditionalselectorwillappeartotherightofit.Eachchoiceofthenewselectorwillcorrespondtoalink,andwillbelabeledwiththelinknameifthereisone,and/orthenameoftheparentnodeitcomesfromifthelinkisnotdisconnected.

ThepurposeofaddingalinkdelayisforcreatingadynamicBayesnet.

Note:Youcanalsosetlinkdelaysby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickinga=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_link.htm');returnfalse;">selectionoflinksandchoosingDelay.

Author–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoAuthor,youcanenterorviewtheauthororsourceofinformationspecifictoanode.

ThisisausefulfunctionwhentherearemultiplepeopleinvolvedinbuildingtheBayesnet.

WhenChanged–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoWhenChanged,youcanviewthetimeanddatethenodewaslastchanged,basedontheclockinyourcomputer.Thisvalueissimilartotheonemaintainedbyyourcomputeroperatingsystemforwheneachfilewaslastchanged,butitcanbemoreusefulforBayesnetssinceitactuallyrecordsthetimeofchange,notjustthetimeoffilesaving,anditprovidesaseparatevalueforeachnode.Youcannotchangethisvalue;itisforobservationonly.Ifnovalueappears,itmeansthatthetimeofthelastchangewasnotsavedintheBayesnetfile,andthenodehasnotbeenchangedsincereadingfromfile.

UserDefined–Multi-PurposeBoxWhenthemulti-purposeselectorofanodedialogboxissettoUserDefined,youcanenterandviewuser-definedfieldsofthenode.

HowTo:Forthefirstfield,youwillneedtoclickNewField…twice.Adialogboxwillcomeupaskingyoutoenteranameforthenewfield(Neticawillverifyitmeetstherequirementsofan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname).

Onceanewfieldisdefined,enteritsvalueinthelargetextspace.Youcanenteranumberoranytext;ifthetextislong,youmightwanttopasteitin.ContinueenteringnewfieldsorclickOkaytoexitthenodedialogbox.

Removal:Ifyoumaketheentryempty,thenNeticawillaskyouwhetheryouwantittobeafieldsettoempty,orwhetheryouwantthefieldremoved.

BetterWay:Formanyoperationsonuser-definedfields,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickmenusofferamoreconvenientmethod.

NodeTablesThefollowingchapterdiscussesthetablesrepresentingtherelationshipbetweennodesandtheirparents,andhowtovieworchangethosetables.Youcanpagethroughtheentirechapterusingthebrowsebuttonabove,seeawrittendescriptionofwhereinformationis,orjumpdirectlytooneofthefollowingtopics:

•TableDialogBox•MeaningoftheTables•ChangingTableEntries•ButtonsintheTableDialogBox•NodeSelector•Deterministic/ChanceSelector•KindsofTables•ScrollingandNavigating•EmptyCells•CellsContainingX•Selecting,CopyingandPastingCells•TableMenuCommands•ChangingColumnOrder•MultipleDialogBoxesforOneNode

TableDialogBoxPurpose:YouusetheTableDialogBoxtoenter,changeorviewthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationshipofanodewithitsparents(i.e.its=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTs).Choosingwhichnodesaregoingtobethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsisnotdonewiththisdialogbox,butratherbyaddinglinks.Anodedoesnotspecifyarelationwithits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">childnodes,sincethoserelationsarespecifiedatthechildnodes.Ifyouwanttherelationtobespecifiedbyan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equation,orifyouwanttochangethepropertiesofanode(e.g.itsname,orwhatstatesithas),usethenodedialogboxinstead.

Obtaining:Obtainatabledialogboxforanodebyselectingit,andthenchoosingTable→View/Edit,clickingthetoolbuttonwiththe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_relation_symbol.htm');returnfalse;">relationsymbol: ,orby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthenodeandchoosingTable.

Table:Therelationshipisexpressedintheformofatable.Thefollowingdescribeswhatthetableentriesmean,howtochangethem,howtoselect,copyandpastethem,howtoscrollandresizethetable,andhowtoreorderitscolumns.

KindsofTables:Thetabledialogboxcanbeusedtovieworeditseveraldifferentkindsoftablesforthenode,whichyouchoosewiththetableselector.Thenode's=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontableorconditionalprobabilitytable(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPT)arethemostcommonlyused,butifyouhaveNeticalearningfromdataorconnectingtoadatabase,thenits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_experience.htm');returnfalse;">experiencetable,unnormalizedprobabilitytableandcountstablewillbeofinterest.

Controls:Makingachangewithinthedialogboxdoesnotaffectthenodeuntilthecorrectbuttonispressed.Thereareselectorstochoosethenodetoworkon,andtomakeitdeterministicorprobabilistic.Thereareseveralmenucommandsthatcanmodifythetable.

Multiple:Youmayhaveseveraltabledialogboxesonthescreenatthesametime,andyoumayalternatebetweenusingdifferenttabledialogboxes,differentnodedialogboxes,andworkingdirectlyinthenetwindow.Touseoneofthetabledialogboxesitmustbethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activewindow.Youmayevenhavemorethanonetabledialogboxforthesamenode.

MeaningoftheTablesForaBayesordecisionnettobefullyspecified,everynatureandutilitynodemusthaveafilled-intable.Eachtableexpressesthevalueofthenodeintermsofits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parents(orasaconstantifthenodehasnoparents).Ifthenodeis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicthenthetablewillbeafunctionwhichprovidesavalueforthechildforeachpossibleconfigurationofparentvalues.Ifthenodeisprobabilistic(i.e.a=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_chance_node.htm');returnfalse;">chancenode),thenthetablewillprovideaprobabilityforeachstateofthechild,foreachpossibleconfigurationofparentvalues.

Forexample,supposenodeA(whichcantakeonvaluesLow,MediumorHigh)andnodeB(whichcantakeonvaluesTrueorFalse)arethetwoparentsofnodeC(whichcantakeonvaluesSmall,MidsizeorLarge).ItisbesttothinkoftherelationbetweenthemasbeinglocatedatnodeC(thechild),anditstabledialogboxmightlooksomethinglikethis:

Ontheleft-handsideisaverticallistofalltheconfigurationsofparentvalues.Ontheright-handsideisonecolumnforeachstateofC.ThenumbersinthetableprovideconditionalprobabilitiesforthevaluesofC,giventhattheparentstakeontheconfigurationoftheirrow.Forexample,the10.000(percent)intheupperleftcornermeansthatP(C=Small|A=Low,B=True)=0.1.Thenumber3.2e-12atthebottomrightmeansP(C=Large|A=High,B=False)=3.2x10^-14.

Emptycellsindicateprobabilitiesthathavenotyetbeenspecified.Examplesarethetwoblankcellsonthethirdrow.

CellswithXindicateanimpossiblecondition.Forexamplethethreex’sonthefifthrowindicatethatthedesignerbelievesthattheconditionA=HighwhileB=Trueisimpossible.

ChangingTableEntriesPurpose:Youwilloftenbringupatabledialogboxjusttoviewtherelationitrepresents.Forexample,ifyouhavejustsolvedadecisionnet,youcanuseittoviewtheoptimaldecisionfunctionsthatNeticahasfound.However,itsmainpurposeistoenterorchangenoderelationswhenbuildingaBayesnetordecisionnet,ordoingwhat-ifanalysiswithanexistingnet.

Deterministic:Ifthedialogboxisforadeterministicrelation,thenyouchangeatableentry(alsoknownasacellofthetable)simplybyclickingdownontopofit,andthenmakingachoicefromthepop-upmenuwhichappears.

Probabilistic:Ifthedialogboxisforaprobabilisticrelation,thenyouchangeaprobabilitybyclickingonittoselectit,andthentypinginthenewnumber.Oryoucanclickonittoselectit,thenclickwithintheselectionwhereyouwanttochangeafewdigits.Youcanenterthenumbersasdecimalfractions(e.g.0.25)orpercentages(e.g.25)bychangingthetableselector.

Navigating:Whenacellisbeingedited,theinsertionpointwillbeflashingwherenewdigitswillenter.Youcanuse←or→keystomoveitaroundwithinthenumber,andifitgetstotheedgeofthenumber,itwilljumptothenextcellinthatdirection.Furtherpresseswilljumptosubsequentcellsinthatdirection.The↑and↓arrowkeyscanbeusedinthesamewaytojumptocellsaboveorbelowthecurrentlyselectedoreditedcell.PressingtheTABkeyjumpstothe“next”cell,whichisthecelltotherightofthecurrentone,unlessitisattheendoftheline,inwhichcaseitisthefirstcellonthenextline.Anotherwaytonavigate,usefulinlargetables,istopicktheparentvalue.

Multiple:ChooseTable→EnterExperiencetoenteruniformexperiencetablesforall=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectednodesatonce.

ButtonsintheTableDialogBoxApply&Okay:Whenyoumakechangesinthetabledialogbox,theydonotaffectthenodeuntilyouclicktheApplyorOkaybutton.Thenallthesettingsaretransferredtothenodeinthenet.TheApplyandtheOkaybuttonshavethesamefunction,excepttheOkaybuttonalsoremovesthedialogboxaftertransferringthesettings.

Reset:ClickingtheResetbuttonwilltransferthecurrentvaluesfromthenodeinthenettothedialogbox.Therearetwomainusesforthisbutton.Thefirstisifyoumakeamistakewhileyouarechangingthetable,andyouhaven’tyetclickedtheApplybutton,youcan“revert”totheoriginalnodebyclickingtheResetbutton(ifyouhavealreadyclickedtheApplybutton,youshouldmakethenetwindow=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">active,doanEdit→Undo,thengobacktothetabledialogboxandclickReset).ThesecondusefortheResetbuttonistoupdatethetabledialogboxaftersomethingelsehaschangedtherelationofthenode.

Forexample,youmightbesolvingadecisionnetrepeatedly,whilevaryingsomepartofit.Aftereachsolutionyouwanttoseehowtheoptimaldecisionfunctionhaschanged.Youwouldbringupthetabledialogboxforadecisionnode,leaveitup,andaftereachre-solutionofthenetyouwouldclicktheResetbuttontoobservethechangesinthetables.AnotherexampleisthatyouarehavingNeticalearnaBayesnetfromanumberofcasefiles,andyouwanttoobservehowtheconditionalprobabilitieschangeasthelearningprocesscontinues.

Changed*:Ifyoumakeanychangestothetable,buthavenotyetpressedeithertheApplyorOkaybutton,thena*willbedisplayedinthewindow'stitlebartoshowthatthetableiscurrentlydifferentfromthatofthenodeinthenet.Ifinsteadthenodeinthenetischangedbysomethingelse(suchaslearningfromdata,solvinganoptimization,anothertabledialogbox,etc.),thenanasteriskinparenthesisisplacedinthewindow'stitlebar:(*)

Close:IfyouclicktheClosebutton,orthe buttoninthetitlebar,orchooseFile→Closewhilethedialogis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">active,thenitwillberemoved.Ifyoupreviouslymadesomechangesinit,andhaven’tclickedtheApplybutton,Neticawillaskifyouwanttoapplythosechangesfirst.

NodeSelectorYoucanswitchwhichnodeatabledialogboxisfor,byusingitspop-upmenulabeled“Node”.Fromthismenuyoucanchooseanynodeinthenet,andwhenyoudo,thecontentsofthedialogboxwillbecompletelyre-adjustedforthenewnode.

Ifyouhavemadechangesinthedialogboxbeforeswitchingnodes,andhavenotyetpressedtheApplybutton,thenamessagewillbepresentedaskingifyouwanttoapplythechangesbeforeswitchingnodes.

Deterministic/ChanceSelectorThetabledialogboxhasaselectorthatallowsyoutomakeanaturenode=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_chance_node.htm');returnfalse;">probabilistic(i.e.achancenode).Ifyouusethisselectorbeforeyouhaveenteredanythingintothetable,itwilljustmodifythedialogboxtobesuitableforenteringdeterministicorprobabilisticinformation.Ifyouhavealreadyenteredarelation,thattablewillbeconverted.

Convertingadeterministictabletoaprobabilisticrepresentationissimple:eachrowoftheresultwillconsistofallzeroes,exceptasingle100%entryatthestatetheoriginaldeterministicfunctionmappedto.

Convertingaprobabilisticrelationshiptoadeterministiconegenerallylosessomeinformation.Foreachparentconfigurationthedeterministicvaluewillbethestatethatwasmostlikelyintheprobabilistictable(i.e.hadthehighest=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobability).

KindsofTablesThetableselector allowschoosingbetweenthedifferenttypesoftablesthatanodecanhave:afunctiontable,conditionalprobabilitytable(viewedwithdecimalorpercentagenumbers),experiencetable,unnormalizedprobabilitytableandacountstable.

Can'tSet:Theonlytypeoftablethatadeterministicnodecanhaveisafunctiontable,soifthedeterministicselectortotheleftofthetableselectorissetto"Deterministic",anychoiceofthetableselectorotherthan"Function"willjustresultinabeepandanexplanatorymessagegoingtothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindow.Iftheleftselectorissetto"Chance"instead,thenanychoicefromtherightselectorisokay,except"Function",whichisthentheonethatresultsinabeep.

FunctionTable:Thefunctiontableallowsonlyasingleoutputvalueforeachpossiblesetofparentvalues(i.e.amathematical"function").Ifthenodeisdiscrete,thenthereareafinitenumberofchoicesandNeticaletsyouenterthembyclickingonatablecellandthenchoosingfromapopupmenu.Ifthenodeiscontinuous,notdiscretized(suchasautilitynode),thenNeticaletsyouenterarealnumberineachcell.

ConditionalProbabilityTable(CPT):Thesearethemostcommontablestoworkwith,andaredescribedindetailontheotherpagesofthischapter.Theyprovideaprobabilityforeachstateofthenode,giventheconditionspecifiedbytherow(i.e.eachparentnodehavingsomevalue),sotheprobabilitiesofeachrowmustsumtoone.Youcanenterthemasdecimalfractionsorpercentages,dependingonwhetherthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_selector.htm');returnfalse;">tableselectorissettoProbabilityor%Probability.

ExperienceTable:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_experience.htm');returnfalse;">Experience

tablesprovideoneconfidencenumberforeachrowofthetable.Experiencenumbersmustnotbenegative,andanexperienceofzerocorrespondstoanimpossiblecondition(arowofXsintheCPT).Experiencenumbersmeanapproximatelytheequivalentnumberofmatchingcasesseen.Experiencenumbersaregeneratedasthenormalizationfactorsofthe"Unnormalizedtable",whichinturnistheCountstablewithaconstantbaseexperienceaddedtoeachcell(usually1).

CountsTable:Thesearetheactualcountsofmatchesduringthelearningprocess,sotheyaregenerallyintegers(e.g.therewere7instancesmatchingthistablecell).However,theywillhaveafractionalpartifthecasefilehada"NumCases"columncontainingfractions,alearningdegreeotherthan1wasused,thetablewashardenedorsoftened,amoreadvancedlearningalgorithmlikeEMorgradientdescentwasusedorafractionalstartingexperiencewasenteredbeforelearning.

ScrollingandNavigatingSinceanodemayhaveverymanyparentconfigurations,theyoftenwon’tallbevisibleinthetabledialogboxatonce.Youcanusethescrollbarstoviewwhateverpartofthelistyouarecurrentlyinterestedin.TheHOME,END,PAGEUPandPAGEDOWNkeysmaybeusedaswell.

Resizing:Youcanalsoresizethetabledialogboxtomakeitbiggerorsmallerbyclickingintheboxatthelowerrightcorner,oronthewindowedgeanddraggingtothenewsize.Whenyoufirstbringupthetabledialogbox,itisconstructedwithasizetomatchthetablesrequiredforthenodeitsfor.Ifyouchangewhichnodethedialogboxisfor,itissometimesconvenienttoresizethedialogboxaswell.

LargeTables:Tablesfornodeswithseveralparentsmayhaveagreatnumberofrows,makingitdifficulttoscrolltotherowyouwant.By=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonastate-namewithinarow,andchoosinganewstatenamefromthemenu,thetablewillautomaticallyscrollsothatanewrowreplacesthatsameposition.Thenewrowwillhaveallparentswiththesamestateastheoriginalrow,exceptthestatethatwaschanged.Bystartingwiththeleft-mostcolumnandsettingastateforeachcolumn,anysettingofparentvaluesmaybeobtained,scrollingtorevealthatrow.Youcanchangewhetheryouwantthetablebasedonstatenames,statetitles,ornumericlevelsbymakingachoiceabovethedividinglineofthemenuthatappearswhenyouright-click.

Remember,youcanalsochangetheorderofcolumnsifyouwantto.

EmptyCellsIfacellofthetabledialogboxtableisblank,itmeansthatthevalueofthecellhasnotbeenspecified.YoumaybebuildingupanetoveranumberofsessionswithNetica,andyoucanusetheemptycellstokeeptrackofwhichpartsofthetablehavenotyetbeenentered.

Newtablesstartoutwithallemptycells,andyoucansetanycellorgroupofcellstoemptybyselectingthecellsandthenpressingtheDELETEkeyorchoosingEdit→Delete.Ifthenodeisdeterministic,youcansetacelltoemptybychoosing“Unknown”fromthepop-upmenuwhichappearswhenyouclickonthecell.

Ifyoudoinference(e.g.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating)withanetthathasnodetableswithemptycells,Neticawillconsiderthemtobeuniform,andgiveyouawarning=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">message.Neticacanfindanddisplayallthenodeswhosetableshaveoneormoreemptycells.(moreinfo)

CellsContainingXMeaning:AcellofthetabledialogboxtablewithjustanXinitindicatesthatnovalueisrequiredforthecell,becausethatconfigurationofparentvalueswillneveroccur.Itactuallydoesn’tsayanythingabouttherelationshipathand,butjustthatwhoeverwasbuildingtheBayesnetdidn’tfeelitwasnecessarytoenteravaluebecauseinthecontextoftheoverallnetitisnotrequired.IfNeticaislaterdoinginferenceanddiscoversthatconfigurationofparentvaluescanoccur,itwillalertyouwithamessageinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">messageswindow.

Importance:Ifyouputanyarbitraryvalueinsuchacell,allinferenceresultswillbethesame,becausethevaluewillnotbeused.Thebestvaluetoputinthecellisthetruevaluethatwouldbeapplicableiftherelationshipbetweentheparentswasdifferent,butifthatvaluedoesn’texist,oryoudon’tknowit,ordon’thavetimetodetermineit,itismuchbettertousetheXfeaturethantojustputinanarbitraryvalue,forthreereasons.First,duringinferenceNeticaperformsanimportantcheckforyouastowhethertheconfigurationisreallyimpossible.Second,itdocumentsyourunderstandingatthetimeyouwerebuildingtheBayesnetforanyoneelsewholaterworkswithit.Third,ifyoulaterchangeotherpartsofthenet,oryoucopyandpastethisnodeintoadifferentnet,orputitinanetfragmentlibrary,thoseparentconfigurationsmaybecomepossible.

Setting:YoucansetacelltoXbyselectingthecellandthentypingX(foraprobabilistictable),orbychoosing‘Impossible’fromthecell’spop-upmenu(foradeterministictable).Forprobabilistictables,ifonecellhasanX,thenallthecellsinthatrowmusthaveanX(becausetheyallcorrespondtothesameparentconfiguration).

GettingCPTsfromTextFilesIfyouwantNeticatolearntheCPTsbasedondatarecordsintextfiles,seethechapteronlearninginstead;hereweobtainactualprobabilitynumbersdirectlyfromtextfiles.

Thereareafewwaysto"import"entireCPTstothenetworkfromfiles:

1.Cut&Paste:Ifthetableisintab-delimitedform,witheachrowcorrespondingtothevariousstatesofthechildnode,youcanjustpasteitintothetabledialogboxforthenode.First,readthetablewithatexteditingprogram(e.g.wordprocessor,orchooseFile→OpenasText).SelecttheentiretableandchooseEdit→Copy.

Thenopenthetableeditorforthechildnode(Table→View/Edit),andselecttheupperleftcell(byright-clickingit,orbyleft-clickinganddraggingatinydistancewithinit).Thecellshouldturnblack.FinallychooseEdit→Paste,andtheentiretablewillbefilled.

Yourtableinthetextfilemustusethesameorderofparentsasinthetabledialogbox.Iftheyaren'tthesame,youcanadjustthecolumnsbeforehandjustbyclickinganddragginginitsheading.

Youcanalsocopyandpasteinasimilarwayfromaspreadsheetprogram,suchasExcel.

2.Makeasimulated"casefile":with1rowforeachentryoftheCPTtable(i.e.theCartesianproductoftheparentsandthechildnodeitself).Thatmeansthatifthechildnodehasnstates,therewillbentimesasmanyrowsinyoursimulatedcasefileastherearerowsintheCPTtable.

ThefirstcolumnofthecasefileshouldbeNumCases,andinthatcolumnyouplacetheCPTprobabilities.

ThenchooseCases→Learn→IncorpCaseFile,anditwillreadtheprobabilitiesinasthefrequencyforeachcase.YouwillneedtoTable→Hardenwithadegreeof1afterwards.Or,youcanmultiplyalltheprobabilitiesinthecasefilebysomelargenumber(thesamenumberforone),soitisasifyouarepresentingNeticawithasetofcaseswhoseprobabilitydistributionmatchestheCPTnumbers.

3.Usea.dnefile:SavetheBayesnetasa.dnefile(fromtheSaveAsdialogbox,choosednefromthemenuinthebox,ormakethefilenameendwith.dne).Thenopenthe.dnefilewithatexteditor.Itwillbequitereadable,andyoushouldeasilybeabletofindthetableforthenodeinquestion.(ifthereisnotablethere,youmaywanttocreateadummytableinNeticabeforehandwithTable→Uniform).Simplycopythewholetableastext,andthenpastetoreplacethetableinthe.dnefile.Thetableinyourtextfilemustbecomma-delimited,witheachrowcorrespondingtothestatesofthechildnode,andtherowsinodometerordercorrespondingtothesameorderofparentnodesasisshowninthe.dnefile(youcanre-ordertheparentsasdescribedabove).Don'tworryaboutthecommentsthatwereoneachlineofthe.dnefile(i.e.,thepartsstartingwith"//");theyaren'tneeded.

4.WriteaProgram:Ifyouwantittobeanautomatedprocess,youcanwriteaprogramthatreadsthetextfile,andthendoescallstoNeticaAPItofilltheCPTTables.

Selecting,CopyingandPastingCellsTodooperationsonasubsetofcellsinthetabledialogbox,youfirstselectthem,whichwillhilitethem.

Selecting:Toselectcellsofanumerictable,clickdowninonecell,anddragthemousetoanothercellbeforereleasingthemousebutton.Whileyouaremovingthemouse,allthecellsintherectanglebetweentheoriginalcellandthecurrentmousepositionwillbehilited.Thecellyoufirstclickdowninmustnotbethecellyouarecurrentlyediting(i.e.theonlyselectedcell,orthecellwiththeinsertionpointblinkinginit)orNeticawillthinkthatyouaredoinganoperationtoeditjustthatcell.Youcandragoutsidethewindowboundarytoforceautoscrolling.Onceaselectionismade,youcanholddowntheSHIFTkeywhileyouclickonanothercelltoextendorreducetheselection.Toselectwholerowsatatime,clickattheleftedgeoftherow(justtotherightofthedoubleline)anddragupordown.

Deterministic:Selectingcellsofadeterministictableisdoneinthesameway,exceptonlyselectionbyrowsisallowed(ifyouclickdowninacellyouwillgetapop-upmenuinstead).

Copy&PasteMultiple:Afteryouhaveselectedsomecells,youcancopytheirvaluestothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboardbychoosingEdit→Copy(orpressingashortcutkey,orclicking ).Toplacethosevaluesinsomeothercells,selectthecellsandchooseEdit→Paste(orpressCTRL+Vorclick ).Ifthepasteregionislargerthanthecopyregion,thecontentsofthecopyregionwillberepeatedhorizontallyand/orverticallytofillthepasteregion(youwillbegivenanoticeiftheyarenotanevenintegermultiple).Ifthepasteregionissmallerthanthecopyregion,youwillbegivenanoticeandthetruncatedcontentswillbepasted.Insteadofselectingthewholepasteregion,youmayfinditeasiertojustselecttheupper-leftmostcellofwhereyouwantthecontentspasted.

Copy&PasteSingle:Selectasinglecellbyclickingdownonitandslightlydraggingthemouse-pointerwithinthecell(ifyoudon'tdrag,Neticawillinsteadpreparethecellforediting),orrightclickthecell.Aswithnodes,youcancut,copyorpastesinglecells.Selectthecellandchooseacommandfrom

theEditmenu,orpresstheequivalentshortcutkey.

OtherPrograms:YoucancopyandpastebackandforthbetweentheNeticatableandaspreadsheet,suchasExcel,orawordprocessingprogram.Ifeachrowofprobabilitiesbeingpasteddoesn'texactlyadduptoone,thendoanormalizecommandafterpasting.Neticacellscopiedtotheclipboardareenteredastext,withatabbetweeneachentryonthesameline,andacarriage-return/line-feedpairattheendofeveryline.Whencopyingfromawordprocessoror=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditortoNetica,theformatshouldbethesame,exceptspace(s)and/oracommamaybesubstitutedforeachtab,andline-feed(s)maybesubstitutedforcarriagereturns.Blanklineswillbeignored.

WholeTablesIncludingNames:TopastewholeCPTtablesintoExcel(oranotherprogram),maketheBayesnetwindow=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activeand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggleonReport→TabSeparatorsandReport→CopytoClipboard(andifdesired,toggleoffReport→ToMessagesWindow).Then=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenode(s)youareinterestedin,chooseReport→CPTTables,clickacellintheExcelspreadsheet,andthenpressCTRL+VorEdit→Paste.YoucancontrolwhetheryouwantthenamesofthenodesandstatesincludedbytogglingReport→IncludeNames.

TableMenuCommandsWhileworkinginatabledialogbox,theTablemenuisoftenuseful.Selectsomecellsorrowsyouwishtooperateon,andthenchooseacommandfromthemenu(ifnocellsareselected,thecommandisappliedtoallthecells).

Table→FillinMissingentersaprobabilityintoemptycellssothattheprobabilitiesofeachselectedrowaddupto1.0(i.e.100%).Anyrowhavingnoemptycells,morethanoneemptycell,orXcellswillsimplybeignored.Thecorrespondingtoolbarbuttonistheonewiththenumberenteringtheemptycell: .

Table→UniformProbabilitieswillsettheselectedrowsofaprobabilitytabletouniformprobabilityvectors,whichmeansthatallstatesofthenodeareequallyprobable.Soallthecellsoftheserowswillcontainthenumber1/(numberofstates),expressedasapercentage.

Table→Randomizeworksonprobabilisticordeterministictables.Fordeterministictablesitsetseachselectedcelltoonepickedrandomlyfromthepossiblestatesofthenode,followingauniformdistribution(i.e.eachstateequallyprobable).Forprobabilistictablesitsetsthecellsofeachselectedrowtorandomlyselectedprobabilities.Ofcourse,theprobabilitiesofeachrowwilladdto1.0(i.e.100%).Thedistributionoftheprobabilitiesenteredisnotuniform(itfavorsnumberscloserto0inanattempttobettermatchrealisticdistributions).Thecorrespondingtoolbarbuttonhasonedieoverthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_relation_symbol.htm');returnfalse;">relationsymbol:

Table→Removewillconvertalltheselectedcellstoemptycells.Ifthereareselectedcells,thenpressingtheDELETEkeywillhavethesameeffect.Thetoolbarbuttonconsistsofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_relation_symbol.htm');returnfalse;">relationsymbolcoveredbyaredX:

Table→BuildFromOtherNetwillbuildthecptsofyourcurrentnetbasedonthecptsofanothernet.Moreinfo

Manyofthesecommandscanalsobedonefromthenetwindow,withoutusinganytabledialogbox,byselectingthenodesofinterest,andthenchoosingthemenucommandfromtheTablemenu.Itwillapplytotheentiretableofalltheselectednodes.

ChangingColumnOrderYoucanusethetabledialogboxofanodetochangetheorderingofitsstates,andofitsparents.Thiscanbeveryusefulforviewingandeditingthetables,andNeticawillmakeallrequiredre-arrangementstotablestoensurethatinferenceresultswillnotbeeffected.

HowTo:First,bringupthetabledialogboxforanode(e.g.by=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonit,andchoosingTable).Clickdownonthenameofthestateorparentnodethatyouwishtomoveinthegraybarofcolumntitles.Themousepointerwillturnintoadoublearrowasyouholddowntheleftmousebutton.Youcandragthecolumntitletoitsnewposition,thenreleasethemousebutton.

Whenyouchangetheorderofthenode'sstatesinthedialogbox,thatchangeimmediatelyeffectsthenodeinthenet,withoutpressingtheApplyorOkaybutton.Toreversetheeffectofthere-ordering,makethenetwindow=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">active,andperformaregular"Undo",forexamplebychoosingEdit→Undofromthemenu.

Whenyouchangetheorderofthenode'sparents,thestructureofthetablewillbesuitablychangedwithinthetabledialogbox.Thenewarrangementofprobabilitiescansometimesprovideusefulinsights.Ifyouareeditingthetable,thenewarrangementofrowsmaymakeiteasiertoselectadesiredrangeofrowsforsomeoperation,ortocopyandpasterangesofrows.WhenyoupresstheApplyorOkaybutton,theneworderingwillbetransferredtothenodeinthenet,sothatinthefuturewhenyoubringupthetabledialog,itwillhavethatordering.Asusual,youcanalways"undo"fromthenetwindow.

Sinceeachtabledialogboxmaintainsitsownparentordering,youcanhavemorethanonedialogboxopenatatimeforasinglenode,withadifferentparentorderingineachone,andworkandviewinterchangeablybetween

them.Inthatcasethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_changed_indicator.htm');returnfalse;">changedindicatorcanbeveryusefulforkeepingtrackofwhatisgoingon.

MultipleDialogBoxesforOneNodeYoumayhavemorethanonetabledialogbox(ornodedialogbox)forthesamenode.Thiscanbeconfusingifyouarenotcareful,soitisnotrecommendedunlessyouneedit(Neticawillaskyoubeforehand).

However,insomesituationsitisveryuseful.Eachdialogboxstoresallthesettingsforitsnodeanddoesn’tlosethemwhenyoumakechangesinanothernodedialogboxortothenodeitself(unlessyoupresstheResetbutton).Soyoucanhaveseveraldifferentsettingsforanode,onesetineachdialogbox,andalternatebetweenthemjustbypressingtheApplybuttononthedialogboxofchoice.Ofcourseyoucandoallkindsofotheroperationsinbetween(suchascompilingthenet,savingittoafile,makingqueries,undoinganoperation,etc.).

Youopenmultipledialogboxesforanodeinthesamewayasyouopenasingledialogbox.Justdotheactionrepetitivelywithoutclosingthepreviousdialogboxesfirst,andanswer‘no’tothequestionofwhetheryouwanttobringtheexistingdialogboxtothefront.

CasesThesetofall=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsenteredintothenodesofasingleBayesnetisreferredtoasacase.Acaseusuallyprovidessomeinformationaboutaparticularobject,person,event,thing,etc.

Neticahasfacilitiesforworkingwithcases,includingtheabilitytosaveacase(i.e.allthecurrentpositivefindings)fromaBayesnettoafile.Laterthosefindingscanbere-enteredintotheBayesnetbyreadingthefile.

Casefilesmayconsistofmanycases(actingasadatabase,inwhicheachcaseisadatabaserecord).YoucanuseNeticatolearnthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofaBayesnetfromsuchafileofcases.NeticacanalsogenerateafileofcaseswhichmatchtheprobabilitydistributionofaBayesnet,whiletakingaccountoffindingscurrentlyentered.Thereareanumberofotherwaystocreatemulti-casefiles.

Neticacanpassthroughafileofcases,applyingBayesnetinferencetoeachcasetogeneratenewinformationaboutit,andthensavingthecasewiththeadditionalinformationtoanewcasefile,whichisknownasprocessingcases.ItcanalsouseacasefiletotesttheperformanceofaBayesnet,finding=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_error_rate.htm');returnfalse;">errorrates,logloss,etc.,whichisknownastestinganetwithcases.

Example1:Inamedicalexample,eachcasemightcorrespondtoacertainpatient.Whenyouwanttoworkwithanewpatient,yousavealltheinformationgatheredforthefirstpatientintoacasefilebeforeremovingitfromthenet,perhapsusingthepatient’snameasafilename.Whenitcomestimetoreconsiderthefirstpatient-perhapssomelabresultshavearrived-youjustreadthatperson’scasefile.

Example2:Foranotherexample,eachcasecouldbeapoliticalriding.Thefindingswouldbedetailsaboutthatriding(suchasdemographics,poll

statistics,etc.),andtheBayesnetcouldbeusedtopredictthepercentageofvoteseachpoliticalpartywillgetinthenextelection.Asnewinformationaboutaridingarrived,itscasefilewouldbekeptupdated.

WorkingwithCasesEntering:ToenteracaseinaBayesnet,simplyentereachofitsfindings.

Removing:Toremovethecurrentcasefromabeliefnet,makesurenonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,andchooseCases→RemoveFindings,orclickthe toolbarbutton.Itwillleavethenetwithnofindingsentered,andifitisan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_auto_update.htm');returnfalse;">auto-updatingnet,thenitsbeliefswillbeupdatedtoreflectthat.IfsomenodesareselectedwhenyouchooseRemoveFindings,thenonlythefindingsforthosenodeswillbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">retracted.

Saving:Youcansavecasesinfilesandreadthembackin.

Reporting:Tocreateatexttableshowingthecurrentcase,useReport→Findings.UsingotherchoicesontheReportmenuyoucancontrolitsappearanceanddestination.Tolocateallthenodesthathaveanyfinding,orjustalikelihoodfinding,youcanselectthem.

SavingandReadingCasesSaving:Tosaveinafileallthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsfromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenet,makesurenonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,chooseCases→SaveCaseAs,orclick ,andthenenterthefilename.Ifsomenodesareselected,thenonlythefindingsfortheselectednodeswillbesaved,andNeticawillbeepandputanoticeinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowthatthewholecasewasn’tsaved.Later,ifyoumakechangestothecaseyoucanchooseCases→SaveCase.

SavingMulti-case:CurrentlyNeticaisunabletosaveacasetoamulti-casefile,butthereareotheroptionsforcreatingmulti-casefiles.

Reading:Tolaterreadthecasebackintoitsoriginalnet,makethatnet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">active,ensurethatnonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,chooseCases→GetCaseorclick andselectthecasefilefromthestandarddialogboxwhichappears.Anyexistingfindingsinthenetwillberemoved,thefilewillberead,andthefindingsenteredintothenet.Ifthenetis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_auto_update.htm');returnfalse;">auto-updating,thenbeliefupdatingwillbedoneautomaticallytoaccountforthefindingsof

thecase.

IfsomenodesareselectedwhenyouchooseCases→GetCase,thenNeticaonlyremovesfindingsandreadsnewonesfortheselectednodes(italsobeepsandputsanoticeinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowthatthewholecasewasn’tread).

Youcanalsoreadacasefromthecommandline.

ReadingMulti-case:Ifyoureadfromafilewithmorethanonecaseinit,thenNeticawillaskyouwhichcaseyouwant.PressingSHIFT+F8getsthepreviouscase.IfthecasefilestoresIDnumsthenNeticawillaskforone,otherwiseitwillaskforthepositionofthecase.

PressingtheF8keygenerallyproducesthesameresultaschoosingCases→GetCasefromthemenu,exceptifacasehasjustbeenreadfromamulti-casefile.ThenF8willautomaticallygetthenextcasewithoutopeninganydialogboxes,whichmakesitconvenienttobrowsethecasesonebyone.Neticaprintsthecase’snumberintheMessageswindow.

DifferentNet:Itispossibletoreadacaseintoadifferentnetthantheoneitwasoriginallysavedfrom.Findingsfromnodesoftheoldnetwillbeenteredintonodesofthesamenameinthenewnet(thetitlesofthenodesareignored).Thestatenamesofthenodes(ifpresent)shouldalsobethesame.Anyfindingsnotcorrespondingtoanodeinthenewnetwillsimplybeignored.Allnamecomparisonsarecase-sensitive.

NumericValues:Realnumbervaluesthatyouhave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredasfindingsfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizedcontinuousnodesaresavedincasefiles,ratherthanjustthestatetheycorrespondto.Thisenablesreadingthecaseintoanothernetwhosenodeforthatvariablehasbeendiscretizedinadifferentway.

MissingState:Ifyoureadinacase,andthecasefilehasavaluethatisn’t

anyofthestatesofthecorrespondingnodeinthenet,thenanerrormessagewillbedisplayed.Forexample,ifnode‘color’hasthestates‘red’and’green’,andinthecasefilethevalueforcoloris‘blue’,themessagewillbedisplayed.Anexceptiontothisoccursifoneofthestatesofthenetnodeisnamed‘other’.Thenthecasewillbereadwithouterror,andthefindingforthenodewillbe‘other’.(moreinfo)

CreatingCaseFilesIfyouwanttocreateacasefilecontainingasinglecase,youcanjustenterthecaseasfindingsintoaBayesnet,andthensaveittofilefromNetica.Tocreateafilecontainingmanycases,thereareseveraloptions.

WordProcessor:Onepossibilityistousea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditororawordprocessingprogram,andmanuallyconstructitaccordingtotheCASE-1format.Besuretosaveitasa“TextOnly”fileifyouuseawordprocessingprogram.

Spreadsheet:IfthedataisinaspreadsheetprogramsuchasExcel,usuallyyoucanjustcopythedatafromthespreadsheettothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboard,andthenpasteitintothetexteditorwindow,anditwillcomeoutintherequiredformat.YouwillhavetoaddthetwoheaderlinesdescribedintheCASE-1format.Oryoucanexportitfromthespreadsheetastext.Inthatcaseyoumayonlyhavetoaddthe“//~>[CASE1]>~”headerline.Alternatively,youcanlearnfromExcel.

Database:Mostdatabaseprogramshaveanoptiontoexportdatainthefromof“flatfiles”oftext.Suchfilesaresuitableascasefiles,withtheadditionoftheheaderlinesdescribedabove.

Simulation:Ifyouwishtocreateamulti-casefileconsistingofrandomcasessampledfromtheprobabilitydistributionrepresentedbyaBayesnet,Neticacanmakeitautomatically.

Programming:Anotherwaytocreateamulti-casefileistowriteacomputerprogramthatcreatesit.Usingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPIProgrammer’sLibraryisespeciallyusefulforthispurpose,sinceitcancreatesuchafilewithjustafewfunctioncalls.Itcanalsobeusedtoupdateand

otherwisemaintaincasefiles,andtoreadthemanddoBayesnetlearningandinferenceusingthem.

CaseFileFormatStructure:Casefiles(single-caseormulti-case)arepureASCII=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_file.htm');returnfalse;">textfiles.Theymaycontain“//~>[CASE1]>~”oratime-authorstamp,somewhereinthefirst3lines,butthatisnotnormallypresent.Thencomesalineconsistingofheadingsforthecolumns.Eachheadingcorrespondstoonevariableofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">case,andisthenameofthenodeusedtorepresentthevariable(sometimesthevariablesarecalledattributesandtheentriesinthecolumnvalues,i.e.attribute-value).Theheadingsareseparatedbyspacesand/ortabs(itdoesn’tmatterhowmany).Thereshouldbenospacesinthenamesofthenodes.

Thecasedataisnext,withonecaseperline(asingle-casefileonlyhasonesuchline).Thevaluesofthevariablesareinthesameorderastheheadingline,andareseparatedbyspacesortabs(thecolumnsdon’thaveto“lineup”astheydointheexamplesbelow).

Discrete:Thevalueofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariableisgivenbyitsstatename,orbyitsstatenumberprecededbya‘#’character(thefirststateis#0).Usingthestatenamesispreferred,sincetheorderofthestatesmaybechangedsometime,andthatwouldrenderafilewithstatenumbersinvalid.The‘#’symbolisrecommended,butmaybeomittedifthenodehasnodiscretizationorvaluesdefined.

Continuous:Thevalueofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousvariableisgivenbyanumberininteger,decimal,orscientificnotation(e.g.-3.21e-7).Ifithasbeen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretized,then

thevaluemaybegivenbyastatenameorstatenumberinstead,butthecontinuousnumberispreferredifitisavailable.Thatwaythecasefilecanbeusedfordifferentdiscretizationsofthatvariableinthefuture.Itisbestifthevaluehasthecorrectnumberofsignificantfigures,sincefutureversionsofNeticamayusethisinformation.

Missing:Ifthevaluesofsomeofthevariablesareunknownforsomeofthecases,thenanasterisk*isputinthefileinsteadofthevalue.Thisisknownas“missingdata”.Whenreadingcasefiles,Neticacanalsounderstandaquestionmark?usedformissingdata.

UncertainorNegative:Negative,interval,Gaussian,set,etcfindingscanalsobeenteredinacasefileusingtheUVFformat.

Comments:Theremaybeasmanyspacesortabsattheendofalineasdesired,andtheremayalsobeC/C++/Javastylecomments(e.g.adoubleslash“//”,followedbyanytext).

IDnum:Therearetwospecialcolumnsthatafilemayhavewhichdon’tcorrespondtonodes.Oneprovidesanidentificationnumberforeachcase,whichmustbeanintegerbetween0and2billion.Theheadingforthiscolumnis“IDnum”.Identificationnumbersdonothavetobeinorderthroughthefile.Themissingdatasymbol*mustnotappearinthiscolumn.

NumCases:Theotherspecialcolumnhastheheading“NumCases”,andindicatesthefrequencyormultiplicityofthecase.Amultiplicityofmindicatesmcaseswiththesamevariablevalues.Itisnotrequiredtobeaninteger,soitcanbeusedtorepresentafrequencyofoccurrenceifdesired.Themissingdatasymbol*mustnotappearinthiscolumneither.

Examples:Hereisalistingof“ChestClinic.cases”.Itinvolvesonlydiscretenodeswithstatenames,andhasanIDnumcolumn,butnofrequencycolumn.Hereisanotherexampleofacasefile,thistimeforcarsbroughtintoagarage.Ithasdiscreteandcontinuousvariables,statenumbersandstatenames,andasterisksformissingentries.

Future:FutureversionsofNeticawillsupportmoreadvancedoperationswithcases,includingamoreefficientfilerepresentation,andawayofusingBayesnetsas“indexingfunctions”todothekindoflookupcommonincase-basedreasoning.However,theabovedescribedtypeoffileformatwillalwaysbesupportedaswell.

CaseFileswithUncertainValues–UVFFormatThecasefilesdiscussedinpreviouspageshaveonlyhadvaluesthatwerecompletelycertain(orcompletelymissing).ButNeticacanalsocreateandreadcasefileshavingvaluesthatareknownwithlimitedaccuracy,oronlyknowntowithinsomelikelihood.Infact,Neticahasaveryelegant,practicalandpowerfulwayofexpressinguncertainfindings,calledtheUVFformat.

WhenNeticareadsinacasecontaininguncertainfindings(forexample,bychoosingCases→GetCase),itwillenterthemintheBayesnetaslikelihoodfindings,soanyprobabilisticinference,nodeabsorption,sensitivityanalysis,etc.willproperlyaccountforthem.Also,theoperationsoncasefiles,suchaslearningfromcases,testnetwithcasesandprocesscases,willworkproperlyoncasefilescontaininguncertainvalues.Whenlearningfromsuchcases,somelearningalgorithmswillworkbetterthanothers.Formoreinformationonthat,andanexampleofworkingwithcasefileshavinguncertainfindings,seethelearningalgorithmspage.

Belowisalistofthedifferenttypesofuncertainvalues,theirsyntaxinthecasefile,andwhattheymean.Eachtypeofuncertainvaluecanappearanywhereinacasefilewherearegularvaluenormallywould.Forexample,acasefilecouldbearegular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CSV_file.htm');returnfalse;">CSVfile,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_tab_delimited_file.htm');returnfalse;">tabdelimitedtextfile,butwithsomeofthevaluesreplacedwithentrieshavingthesyntaxdescribedbelow.

GaussianSyntax: m+-smandsarerealnumbers

Examples: 5+-23.27+-0.030+-1e-5

Thisisfora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_normal_distribution.htm');returnfalse;">Gaussian(alsoknownas“normal”)likelihoodfinding,wherethemis

themeanandsisthestandarddeviation.Notethattherecannotbeanyspacebeforeorafterthe+-.Theuncertaintiesinmeasurementsfromlabinstruments,orpollingresults,areoftenexpressedwitha±notation,andindicateaGaussiandistribution,sotheycannowbeeasilyinputintoNetica(althoughsometimestheymaymeananintervaldistribution,asdescribedbelow).

IntervalSyntax: [a,b]aandbarerealnumbers,statenamesorindexesprecededby

#

Examples: [0,10][-3,2.27][lo,med][#1,#3]

Theremaybespacesbeforeorafterthecommaorbrackets.Intervalsofstatesincludebothendpoints,so[lo,med]includesstateslo,medandanystatesbetween.Intervalsofnumbersincludethelowerendpoint,butnottheupperendpoint,so[0,10]forvariableXmeans0<=X<10.Likelihoodwithintheintervalisone;outsidetheintervalitiszero.

UnboundedIntervalSyntax: >mor<mmisarealnumber,statenameorstateindexprecededby#

Examples: >4.75<-10<med>#2

Whenmisastate,theintervalincludestheendpoint,andwhenitisarealnumber,theintervalincludestheendpointonlyfor>intervals(so>isreally).Theintervalcanpotentiallyextendtoinfinity,butinpracticewillprobablybelimitedbyknownmaximumorminimumvaluesforthevariable.Likelihoodwithintheintervalisone;outsidetheintervalitiszero.

SetofPossibilitiesSyntax: {s1,s2,…sn}eachsiisastatename,stateindexprecededby#,interval,

unboundedinterval,orGaussian.

Examples: {lo,med}{red,blue,green}{#1,#5,#7}{[0,3.5],[4.5,10]}{[#35,#122],>#500}

Theremaybespacesbeforeorafterthecommaorbraces.Thevaluecanbeconsideredtobeadisjunctionoftheelements(e.g.X=redorX=blueorX=green).Thelikelihoodofelementsinthesetisone;ofthosenotinthe

set,itiszero.

SetofImpossibilitiesSyntax: ~{s1,s2,…sn}eachsiisastatename,stateindexprecededby#,intervalor

unboundedinterval

Examples: ~{lo}~{red,blue,green}~{#1,#5,#7}~{[0,3.5]}

Theremaybespacesbeforeorafterthecommaorbraces,butnotbetweenthetilde(~)andthebrace.Thisisthesameas"SetofPossibilities"exceptthe"possible"statesarethosethatarenotlisted,ratherthanthosethatarelisted.Thelikelihoodofelementsinthesetiszero;ofthosenotintheset,itisone.

A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativefindingcanberepresentedeasilybyjustlistingthestate(s)eliminatedbytheobservation.

LikelihoodSyntax: {s1p1,s2p2,…snpn}eachsiisastatename,stateindexprecededby#,

interval,unboundedinterval,orGaussian.Eachpiisa

numberbetween0and1.Somepimaybeabsent.

Examples: {female.8,male.3}{3+-10.2,7+-20.4}{[0,1.5].5,[1.5,5]0.1,[5,10]0.02}

Thisisthesameasasetofpossibilities,buteachpossibilityisweightedwithalikelihoodthatappearsafterit(separatedbyasinglespace).Themostcommonkindoflikelihoodvectorsarefordiscretevariables,whereeachstateislisted,followedbyitsprobability.Anystatesthatappearwithoutaprobabilityhavealikelihoodof1,andanystatesthatdon'tappearatallhavealikelihoodof0.

Arbitrarylikelihooddistributionsforcontinuousvariablescanbeformedbyaseriesofadjacentintervals,eachwithitsownprobability.Ortheelementscanoverlap,andthentheirlikelihoodsarecombined.Forexample{[0,10].1,[2,4].2}wouldbethecombinationofarectfunctionextendingfrom0to10

withheight0.1,andanotherrectfrom2to4withaheightof0.2.

AnotherusefuldistributionthatiseasytoformistheweightedcombinationofGaussians.Forexample{3+-10.2,7+-20.4}isabi-modaldistributionwithpeaksat3and7.

ItispossibletomixweightedGaussians,intervals,anddiscretestateswithinasingle{...}likelihoodvector.

NegativeLikelihoodSyntax: ~{s1p1,s2p2,…snpn}eachsiisastatename,stateindexprecededby#,

interval,orunboundedinterval.Eachpiisapositivenumber.

Somepimaybeabsent.

Examples: ~{red,green,teal.2,olive.8}~{[0,2].4,[2,6].2}

Thesameasasetofimpossibilities,buteachentryisweightedwithalikelihood,whichappearsafterit.Ifnonumberappearsafterit,itslikelihoodis0.Entriesthathavenumbersabove1areindicatedtobemoreprobablethanthosenotlisted,andentrieswithnumbersbelow1arelessprobablethantheunlistedones(unlistedentrieshavealikelihoodof1).

CompleteUncertaintySyntax: *[i.e.thesyntaxisjustanasterisk]

Ifnothingisknownregardingthevalueofthisvariable(i.e.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdata),thenaquestionmark?oranasterisk*shouldbeusedtoindicatethat.Itisequivalentto~{}whichisalikelihoodofallones.

ExampleCaseFile-ChestClinicAsanexampleofacasefile,hereisalistingof“ChestClinic.cases”whichwasproducedbytheSimulatingRandomCasesexample.Itinvolvesonly=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenodeswithstatenames,andhasanIDnumcolumn,butnofrequencycolumn.(Anotherexample)

//~->[CASE-1]->~IDnum VisitAsia Tuberculosis Smoking Cancer TbOrCa

1 No_Visit Present Smoker Absent True

2 No_Visit Absent Smoker Absent False

3 No_Visit Absent Smoker Present True

4 No_Visit Absent NonSmoker Absent False

5 No_Visit Absent Smoker Present True

6 No_Visit Absent Smoker Absent False

...

119 No_Visit Absent Smoker Absent False

120 No_Visit Absent Smoker Present True

ExampleCaseFile-CarDiagnosisHereisanexampleofacasefileforcarsbroughtintoagarage.NoticeBatAge,whichisacontinuousvariable,Lightswhicharesuppliedbystatenumbersinsteadofnames,andtheasterisksformissingentries:

//~->[CASE-1]->~

Starts BatAge Cranks Lights StMotor SpPlug MFuse Alter BatVolt Dist PlugVolt

False 5.9 False #0 * fouled okay * dead * *

False 1.3 False #0 * okay okay * dead * none

False 5.2 False #0 Okay okay okay Okay dead Okay none

True 4.1 True #2 * okay okay * strong Okay strong

True 2.7 * #2 * wide okay * strong Okay *

* * True #2 * fouled okay * * Okay strong

False 1.7 True #0 Okay okay okay Okay dead * none

True 2.9 True #2 * * * * strong Okay strong

(Anotherexample)

SimulatingRandomCasesYoucanuseNeticatogenerateaseriesofrandom=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">caseswhoseprobabilitydistributionmatchesthatofaparticularBayesnet,whichisknownassimulation(sometimescalledsampling).ThesecasescanbyusedasexamplescenariosofwhatoneshouldexpectiftheBayesnetmatchesreality.Ortheycanbemanipulatedandcombinedwithothercases,andthenusedtolearnanewnet.

Thesamplingalgorithmsusedareprecise,sothatthelong-rangefrequenciesofthecaseswillexactlyapproachtheprobabilitiesoftheBayesnet,whiletakingaccountofallfindingscurrentlyentered.

Thecaseswillbestoredinafilewhoseformatmatchesthespecificationofacasefile.OnceNeticahasmadethecasefile,youcanbrowseitwiththeF8keytoseetheindividualcases.

HowTo:Togenerateacasefileforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activeBayesnet,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compileit,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodesforwhichyouwishtohavevaluesinthecasefile,andthenchooseCases→SimulateCases.Allthenodesofthenetwillbeusedtogeneratethecases,butcolumnswillonlybemadefortheselectedones.Youwillbequeriedforhowmanycasestogenerate,thefilenameforthecasefile,wheretoputit,andhowmuch=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdatayouwant.Normallyyouwillenter0fortheamountofmissingdata,butif

youwanttohaveacasefilewithasterisksforsomefractionofthefields,enterthatfraction(e.g.entering0.25means25%ofthevalueswillbemissing).Ifyouwishtogenerateonlyasinglerandomcase(andnotsavetofile),chooseCases→RandomCase.

Example:Asanexample,ifyoudoaCases→SimulateCasescommandwith‘ChestClinic.dne’fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder,andenter120,“ChestClinic.cases”and0tothedialogboxes,thenyouwillobtainacasefilesimilartothis(thecasefileyouobtainmaybealittledifferent,sincerandomnumbersareinvolved).

WithEquations:Ifoneormorenodeshaveanequationtodefinetherelationbetweenanodeanditsparents,thenyoumaywantNeticatousethoseequationsdirectlytogeneratetherandomcases,insteadoftheprobabilitytableswhichapproximatetheequations.Inthatcase,don’tcompilethenetbeforedoingCases→SimulateCases.Thesamplingprocesswillbeslowifthenethasanunlikelysetoffindingsentered(arejectionmethodisused).Inthecasefilegenerated,continuousvariables(whetherornottheyhavebeen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretized)willhaveasvaluestheircontinuousrealnumberforeachcase,notjustastaterepresentingarangeofvalues.

ProcessCasesNeticacanprocessafileofcases.Foreachcaseinthefile,NeticareadsthecaseandentersitasfindingsintoaBayesnet.ThenNeticadoes=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingtofindprobabilitiesforallthenodesthatdidn'thavefindings.FinallyNeticawritestheresultstoanoutputfile.

Note:Ifthepurposeistogradetheperformanceofthenet,basedonthecases,itissimplertouseTestWithCases.

Note:Ifmorecontrolisneeded,youmaywanttoprogramNeticathroughitsCOMinterfaceusingVisualBasic,JavaorC/C++.

HowTo:First,opentheBayesnetyouwishtouse.ThenchooseCases→ProcessCasesfromthemenu.Thestandarddialogboxforopeningafilewillappear.Fromitchoosethecontrolfile(describedbelow)thatyouwishtouse.WhenyouclickOkay,anewdialogboxforopeningcasefileswillappear,fromwhichyouchoosethecasefiletobeprocessed.AfteryouclickOkay,thedialogboxforsavingafilewillappear,inwhichyouenterthenameofthefileyouwanttheresultswrittento.

Neticawillthenproceedtoprocessallthecases,printingthefractioncompletedinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindow(ifthatisn'tobscuredbytheBayesnetwindow).Ifyouwanttohaltprocessingbeforeitiscompleted,holddowntheCTRLkeyandpresstheleftmousebutton.

Ifthereareanyfindingsenteredintothenetworkbeforeprocessingstarts,thosefindingswillbeusedforallbeliefupdating,evenoverridingfindingsfoundinthecasefile.Ifan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredfindingisgoingtooverridecasefilefindings,youwillbewarnedandaskedifyouwantto=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">retractallfindingsfirst.

ControlFile:ThecontrolfileisatextfilewhichyoucancreatebychoosingFile→New→TextEdit.Youenterinthisfilewhatyouwishtoappearineachcolumnoftheoutputfile(eachrowoftheoutputfileisfortheresultsofonecase).Thechoicesforcolumnsare:

IDnum()freq()finding(<node>)caseprob()bel(<node>,<state>)util(<node>,<state>)belvec(<node>)utilvec(<node>)mostprob(<node>)expval(<node>)best(<node>)stddev(<node>)

where<node>shouldbereplacedwiththenameofanode(notitstitle),and<state>shouldbereplacedwithastatenameforthatnode,ora#symbolfollowedbythestatenumber(e.g.,#0).

IDnum()andfreq()transfertheIDnumandfreqvaluesfromthecasefiletotheoutputfile.finding(<node>)transfersthefindingfromthecasefileifthereisone,otherwiseitplacesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdatasymbol.

caseprob()displaysthejointprobabilityofallthefindingsofthecasetakentogether(andincludinganyfindingsentereddirectlyinthenetbeforeprocessingwasstarted).

bel(<node>,<state>)displaysthebeliefthatthevalueof<node>is<state>.Inotherwords,itputsP(<node>=<state>|findings),wherefindingsare

fromthecase,andthosedirectlyenteredinthenetbeforeprocessingwasstarted.

mostprob(<node>)providesthemostprobablestatefor<node>.

util(<node>,<state>)isforadecisionnode,anditdisplaystheexpectedutilityofmakingdecision<state>.

best(<node>)providesthebestdecisionfor<node>,ifthatisavailable.

belvec(<node>)displaysalistofnumbersinparenthesis,eachseparatedbyaspace,thatarethebeliefsforeachofthestatesof<node>.

utilvec(<node>)isforadecisionnode,anditdisplaystheexpectedutilityofeachdecisionof<node>inaparenthesizedlist.

expval(<node>)displaystheexpectedvalue(i.e.meanvalue)of<node>,andstddev(<node>)putsthestandarddeviationof<node>.Thesemayonlybeusedforcontinuousvariables,orfornodesrepresentingdiscretevariableswhichhavearealnumbervalueassignedtoeachstate(thisisdoneusingthenodedialogbox).

Example:Hereisanexamplecontrolfile:

IDnum()bel(Color,red)bel(Color,blue)bel(Color,green)expval(Cost)

andhereistheoutputfileitcreated:

IDnum P(Color=red) P(Color=blue) P(Color=green) E[Cost]

1 0.000167195 0.0117262 0.988107 6.86929

2 0.422277 0.0130726 0.56465 3

3 0.610178 0.0203665 0.369455 3

4 0.324446 0.0163193 0.659235 5.94723

5 0.000381718 0.0893132 0.910305 3

TestNetUsingCasesThepurposeofthistestistogradeaBayesnetusingasetofreal=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">casestoseehowwellthepredictionsordiagnosisofthenetmatchtheactualcases.Itisnotfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.

First=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodesyoudonotwishthenettoknowthevalueofduringitsinference.Forexample,ifthenetisformedicaldiagnosis,youmightselectthediseasenodeandnodesrepresentingotherunobservableinternalstates.Thesenodesarecalledunobservednodes.

ThenchooseCases→TestwithCases.Youwillbeaskedwhichcasefiletouse,andafteryouchooseone,Neticawillstartprocessing.The=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowwillcometothefrontanddisplaythefractionofcasesprocessedsofar.HolddownCTRL+SHIFT+LEFTBUTTONatthesametimeifyouwanttostopprocessingcasesandprinttheresultsobtainedsofar.

Neticawillpassthroughthecasefile,processingcasesone-by-one.Foreachcase,Neticareadsinthecase,exceptforanyfindingsfortheunobservednodes.Itthendoesbeliefupdatingtogeneratebeliefsforeachoftheunobservednodes.Itgoesbackandchecksthetruevalueforthosenodesassuppliedbythecasefile(iftheyaresuppliedforthatcase),andcomparesthemwiththebeliefsitgenerated.Itaccumulatesallthecomparisonsintosummarystatistics.

WhenNeticaisdone,itwillprintareportforeachoftheunobservednodes.Thesereportsincludeaconfusionmatrix,=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_error_rate.htm');returnfalse;">errorrate,calibrationtable,quadratic(Brier)score,logarithmiclossscore,sphericalpayoffscore,surpriseindexes,and=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_test_sensitivity.htm');returnfalse;">testsensitivity.For=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_binary_node.htm');returnfalse;">binarynodesitalsoreports=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_test_specificity.htm');returnfalse;">testspecificity,predictivevalueandpredictivevaluenegative.Foraneasywaytoproducereceiveroperatingcharacteristic(ROC)plots,seeQualityofTesttopic.

Forfulldocumentationonthisfunction,andthereportsgenerated,seetheTestNetwithCasesChapterinSpecialTopics.

Netica’sLearningYoumaywanttoreadtheintroductiontoBayesnetlearningfromcases.

Neticacanlearnfromafileofcases,oritcanlearnfromcasesone-by-oneasyouenterthem.Itcanalsoconnectdirectlywithadatabase,orlearnfromcasesinExcel.

ThewaythatNeticalearnsreliesontheconceptofexperience.

Ifyouarelearningfromaworldthatisconstantlychanging,andyouwantthenettoadapt,fadingmaybeuseful.

Afterlearningfromsomecases(orperhapsmanuallyconstructinganet)youmaywanttotestitsperformanceusinganothersetofcases.

Neticaversions5.0andlaterallowforbasicstructurelearning.

LearningfromCaseDataBayesnetlearningistheprocessofautomaticallydeterminingarepresentativeBayesnetgivendataintheformof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">cases(calledthetrainingcases).Eachcaserepresentsanexample,event,objectorsituationintheworld(presumablythatexistsorhasoccurred),andthecasesuppliesvaluesforasetofvariableswhichdescribestheevent,object,etc,asspecifiedinthepreviouschapter.Eachvariablewillbecomeanodeinthelearnednet(unlessyouwanttoignoresomeofthem),andthepossiblevaluesofthatvariablewillbecomethenode’sstates.Learningfromcasesdataresultsin=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probability_revision.htm');returnfalse;">probabilityrevision.

Thelearnednetcanbeusedtoanalyzeanewcasewhichcomesfromthesame(orappropriatelysimilar)worldasthetrainingcasesdid.Typicallythenewcasewillprovidevaluesforonlysomeofthevariables.Theseare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredasfindings,andthenNeticadoesprobabilisticinferencetodeterminebeliefsforthevaluesoftherestofthevariablesforthatcase.Sometimeswearen'tinterestedinvaluesforalltherestofthevariables,butonlysomeofthem,andwecallthenodesthatcorrespondtothesevariablestargetnodes.Ifthelinksofthenetcorrespondtoacausalstructure,andthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_query_node.htm');returnfalse;">targetnodesareancestorsofthenodeswith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_findings_node.htm');returnfalse;">findings,thenyoucouldsaythatthenethaslearnedtododiagnosis.Ifthetargetnodesaredescendants,thenthenethaslearnedtodoprediction,andifthetarget

nodecorrespondstoa"class"variable,thenthenethaslearnedtodoclassification.Ofcoursethesamenetcoulddoallthree,evenatthesametime.

TheBayesnetlearningtaskhastraditionallybeendividedintotwoparts:structurelearningand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parameter_learning.htm');returnfalse;">parameterlearning.Structurelearningdeterminesthedependenceandindependenceofvariablesandsuggestsadirectionofcausation,inotherwords,theplacementofthelinksinthenet.Parameterlearningdeterminestheconditionalprobabilitytable(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPT)ateachnode,giventhelinkstructuresandthedata.

YoumightnotwantNeticatolearnthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofallthenodesinyourBayesnet.SomeofthenodesmayhaveCPTsthathavealreadybeenlearnedwell,werecreatedmanuallybyanexpert,orarebasedontheoreticalknowledgeoftheproblemathand(perhapsexpressedbyanequation).Neticaallowsyoutorestrictthelearningprocesstoasubsetofthenodes,andthosenodesarecalledthelearningnodes.

Ifeverycasesuppliesavaluewithcertaintyforeachofthevariables,thenthelearningprocessisgreatlysimplified.Ifnot,therearevaryingdegreesofpartialinformation:

Ifthereisavariableforwhichnoneofthecaseshaveanyinformation,thatvariableisknownasalatentvariableor“hiddenvariable”.

Ifsomecaseshavevaluesforacertainvariable,andothersdon’t,thatisknownasmissingdata.

Somevaluesforvariablesmaynotbegivenwithcertainty,butonlyaslikelihoodfindings.

Itmayseemstrangetobelearninganetthathaslatentvariables,sincenoneofthetrainingcaseshaveanyinformationonthem.Youintroducealatent

variableasaparentnode(orintermediatenode)ofmultiplechildnodes,andNeticausesthecorrelationsamongthechildrentodeterminerelationshipsbetweenthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_latent_node.htm');returnfalse;">latentnodewithothers.TheresultmaybeaBayesnetthatisactuallysimpler(hasfewerCPTentries),andgeneralizesbetter(i.e.performsbetteronnewcasesseen).ForanexampleofusingNeticatolearnalatentvariable,seethe“LearnLatent.dne”netinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">ExamplesfolderofNeticaApplicationdistribution,orgetitfromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsysnetlibrary.

MoreinfoonNetica’slearning.

MoreinfoonLearningAlgorithms.

LearningAlgorithmsTherearethreemaintypesofalgorithmsthatNeticacanusetolearnCPTs:counting,expectation-maximization(EM)andgradientdescent.Ofthethree,“counting”isbyfarthefastestandsimplest,andshouldbeusedwheneveritcan.Itcanbeusedwheneverthereareno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_latent_node.htm');returnfalse;">latentvariables,andnotmuch=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdataoruncertainfindingsforthelearningnodesortheirparents.Whenlearningthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTofanodebycounting,Neticawillonlyusethosecaseswhichsupplyadefinitevalueforthenodeandallofitsparents.

Ifyoucan’tusecounting,thenyoumustuseEMlearningorgradientdescent.Foreachapplicationarea,itisusuallybesttotryeachonetoseewhichgivesthebetterresults.Generallyspeaking,EMlearningismorerobust(i.e.givesgoodresultsinwidevarietyofsituations),butsometimesgradientdescentisfaster.Forallthreealgorithms,theorderofthecasesdoesn’tmatter.

DuringBayesnetlearning,wearetryingtofindthemaximumlikelihoodBayesnet,whichisthenetthatisthemostlikelygiventhedata.IfNisthenetandDisthedata,wearelookingfortheNwhichgivesthehighestP(N|D).UsingBayesrule,P(N|D)=P(D|N)P(N)/P(D).SinceP(D)willbethesameforallthecandidatenets,wearetryingtomaximizeP(D|N)P(N),whichisthesameasmaximizingitslogarithm:log(P(D|N))+log(P(N)).Belowweconsidereachofthetwotermsofthisequation.Themoredatayouhave,themoreimportantthefirsttermwillbecomparedtothesecond.

Therearedifferentapproachestodealingwiththesecondtermlog(P(N)),whichisthepriorprobabilityofeachnet(i.e.howlikelyyouthinkeachnetisbeforeseeinganydata).Oneapproachistosaythateachnetisequallylikely,inwhichcasethetermcansimplybeignored,sinceitwillcontributethesame

amountforeachcandidatenet.Anotheristopenalizecomplexnetsbysayingtheyarelesslikely(whichisofmorevaluewhendoingstructurelearning).Neticabasesthepriorprobabilityofeachnetontheexperienceandprobabilitytablesthatexistinthenetbeforelearningstarts,whichappearstobeauniqueandelegantapproach.Ifthenethasnotbeengivenanysuchtables,thenNeticaconsidersallcandidatenetsequallylikelybeforeseeinganydata.

Thefirsttermlog(P(D|N))isknownasthenet’sloglikelihood,IfthedataDconsistsofthenindependentcasesd1,d2,…dn,thentheloglikelihoodis:log(P(D|N))=log(P(d1|N)P(d2|N)…P(dn|N))=log(P(d1|N))+log(P(d2|N))+…+log(P(dn|N)).Eachofthelog(P(di|N))termsiseasytocalculate,sincethecaseissimplyenteredintothenetas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings,andNetica’sregularinferenceisusedtodeterminetheprobabilityofthefindings.

BothEMandgradientdescentlearningworkbyaniterativeprocess,inwhichNeticastartswithacandidatenet,reportsitsloglikelihood,thenprocessestheentirecasesetwithittofindabetternet.Bythenatureofeachalgorithmtheloglikelihoodofthenewnetisalwaysasgoodasorbetterthantheprevious.Thatprocessisrepeateduntiltheloglikelihoodnumbersarenolongerimprovingenough(accordingtoatolerancethatyoucanspecify),orthedesirednumberofiterationshasbeenreached(alsoaquantityyoucanspecify).Neticausesaconjugategradientdescent,whichperformsmuchbetterthansimplegradientdescent.

References:Tounderstandhoweachalgorithmworks,itisbesttoconsultareference,suchasKorb&Nicholson04,Russell&Norvig95orNeapolitan04.Briefly,EMlearningrepeatedlytakesaBayesnetandusesittofindabetteronebydoinganexpectation(E)stepfollowedbyamaximization(M)step.IntheEstep,itusesregularBayesnetinferencewiththeexistingBayesnettocomputetheexpectedvalueofallthemissingdata,andthentheMstepfindsthemaximumlikelihoodBayesnetgiventhenowextendeddata(i.e.originaldataplusexpectedvalueofmissingdata).GradientdescentlearningsearchesthespaceofBayesnetparametersbyusingthenegativeloglikelihoodasanobjectivefunctionitistryingtominimize.GivenaBayesnet,itcanfinda

betteronebyusingBayesnetinferencetocalculatethedirectionofsteepestgradienttoknowhowtochangetheparameters(i.e.CPTs)togointhesteepestdirectionofthegradient(i.e.maximumimprovement).Actually,itusesamuchmoreefficientapproachthanalwaystakingthesteepestpath,bytakingintoaccountitspreviouspath,whichiswhyit’scalledconjugategradientdescent.Bothalgorithmscangetstuckinlocalminima,butinactualpracticedoquitewell,especiallytheEMalgorithm.

Mostneuralnetworklearningalgorithms(suchasbackpropagationanditsimprovements)aregradientdescentalgorithms.ThatinvitesacomparisonbetweenBayesnetlearningandneuralnetlearning,with=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_latent_node.htm');returnfalse;">latentvariablescorrespondingtohiddenneurons.InthecaseofBayesnetlearning,therearegenerallyfewerhiddennodes,thelearnedrelationshipsbetweenthenodesaregenerallymorecomplex,theresultofthelearninghasadirectphysicalinterpretation(byprobabilitytheory)ratherthanjustbeingblack-boxtypeweights,andtheresultofthelearningismoremodular(partscanbeseparatedoffandcombinedwithotherlearnedstructures).

SingleCaseLearningNeticahastheabilitytorevisethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofnodestoaccountforthecurrentlyenteredcase,aswellassomeotherlearningabilities.

Preparation:Tolearnfromasinglecase,youmustfirsthaveanetconstructed,includingallnodes,statesandlinks.NodesinthenetmayalreadyhavetheirCPTs,whichyouenteredmanuallyorpreviouslylearned,andwhichyounowwanttoimproveusinglearning.OrtheremightnotbeanyCPTs,andyouwanttolearnthemfromscratch.

Doing:IfthecaseisnotalreadyintheBayesnet,youenteritintothenetasfindings.Only=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefindingswillbeused;negativeandlikelihoodfindingswillbeignored.Thenyou=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodeswhoseprobabilitiesyouwouldliketohaverevisedtoaccountforthecase,ifpossible.Usuallyyouwouldlikeallpossiblenodestohavetheirprobabilitiesrevised,soyouwouldselectallthenodes(ordon’tselectanynodes,whichisequivalent).ThenchooseCases→Learn→IncorporateCase,orclickthetoolbarbuttonwhichhasanarrowpointingfromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case_symbol.htm');returnfalse;">casesymboltothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_relation_symbol.htm');returnfalse;">relationsymbol: .

Degree:Youwillthenbequeriedfora“degree”,whichisnormally1.Bymakingit2,youcanachievethesameeffectaslearningthesamecasetwice,andequivalentlyforothernumbers.Bymakingit-1,youcanexactlyunlearnacasethatwasearlierlearnedwithdegree=1,andsoonforothernegative

numbers.Don’ttrytounlearncasesthatwereneverlearned,ortounlearnthemwithgreaterdegreethantheywerelearned.

WhatHappens:Selectednodesforwhichthecaseprovidessufficientdata(i.e.findingsforitandits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parents)willhavetheirprobabilitiesrevisedasmallamounttoaccountforthecase,andtheirappropriateexperiencelevelsincreasedslightly,accordingtoNetica’slearningalgorithm.

LearningFromaCaseFileThisdescribeshowtolearnaBayesnetfromafileofcases(alternately,youcanlearnfromcasesone-by-oneasyouenterthem,ordootherlearningfunctions).Thestepsinvolvedarelistedbelow,followedbymoredetailedinstructions:

1.Obtainafileofcases2.Createnodesforthevariablesofinterest3.Connectthenodeswithlinks4.Learntheconditionalprobabilitytables(CPTs)5.YoumaythenwanttoviewormodifytheCPTs,hardentheCPTs,absorbnodes,orlearnfromfurthercasefiles(whichmayrequirechangingthenamesofnodesorstates,oraddingnewnodesorlinks)

1.CaseFile:SeeCreatingCaseFiles.Note:IfyouareusingNeticaonaMac,itcannotlearncasesfromanExcelfile.YoumustfirstconverttheExcelfileintoatextfileinordertosuccessfullyexecutelearning.Note:besureyourtextfilefollowsproperformatting.

2.Nodes:Beforelearningbegins,youmusthaveaBayesnetwhosenodesarethevariables(i.e.attributes)ofthecases.Itisokayifithasadditionalnodesrelatedorunrelatedtothecasesinthefile.

Ifyoudon’talreadyhaveanetconstructed,orthenetyouhavedoesn’tincludeallthevariablesinthecasefilethatyouwish,Cases→Learn→AddCaseFileNodesmaybehelpful.Itwillscanthroughacasefileandaddtothecurrentnetnewnodesforanyvariablesthatitdiscoversinthecasefilethataren’talreadyinthenet.Thestatesofthenewnodeswillbeallthepossiblevaluesdiscoveredfromthecasefile.Ifyournetalreadyhasanodewiththesamenameassomevariablefromthecasefile,butthatnodedoesn’thaveallthestatesthatarementionedinthecasefileforthatvariable,thenthosestateswillbeaddedtothenode(unlessthenodehasastatecalled‘other’).

AfterNeticahasaddedallthenodes,youmovethemtothepositionsyouwant,anddeleteanythatyouaren’tinterestedin.

3.Links:Addlinksbetweenthenodesinthenettocapturethedependencies

thatyouwishtolearn.Trytoavoidgivinganynodetoomanyparents,especiallyifyoudon’thaveverymanycasestolearnfrom.Alternatively,youcanuseTANlearningtolearnthelinkstructure,givenatargetnode.

4.Learn:WhenyouchooseCases→Learn→IncorpCaseFile,Neticawillaskyouforacasefileanda“degree”.Normally,youenter1forthedegree,butyoucanenterothernumbersforspecialeffects.Ifyouwanttoundotheeffectofearlierlearning,youcanlearnagainfromthesamefile,butwithadegreeof–1(itdoesn’tmatterifyouhavedoneothercountinglearningsincethen,providingyouhaven’thardened,softened,faded,oreditedthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTs).Ifyouenter2forthedegree,thelearningwillactasifitseeseverycaseinthefiletwice,andsimilarlyforothernumbers(fractionalnumbersareokay).NeticabuildsuptheCPTsaccordingtoitslearningalgorithm,andasitprocessesthecases,itreportsitsprogressinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindow.

LearningFromCasesUsingExcelNeticacanlearnthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofnodesdirectlyfrom=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">casesstoredinanExcelspreadsheet(akaworkbook).DescribedelsewhereisNetica’sabilitytolearnfromtextfilesofcases,andNetica’sabilitytolinkwithExceltoexportposteriorbeliefs.

HerearethestepstolearnaBayesnetdirectlyfromanExcelspreadsheet:

1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

Note:ifyouareusingNeticaonaMac,learningfromanExcelfilewillnotwork.Youmustconvertyourcasefileintoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_file.htm');returnfalse;">textfileandthenyoucanproceedwiththestepslistedabove.

LearningFromCasesUsingExcel1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

Structure:Thespreadsheetshouldbearrangedwithcolumnscorrespondingtothevariablesofinterest(bynodename),andeachrowbeingacase(aka"record").Attheintersectionofeachrowandcolumnisthecellthatgivesthevalueofthevariableindicatedbythecolumn,forthecaseindicatedbytherow.

Thefirstrowmustcontainthenamesofthevariables.EachwillcorrespondtoanodeintheBayesnet,althoughtheExcelfilemayhavesomevariablesthatdon'tappearinthenetandvice-versa.Ifdesired,youcangiveeachcaseanidentificationnumber.

RepresentingPriorKnowledge:Tosimplifypriorpercentageknowledgeinyourfile,youcanusetheNumCasesfunctiontodenotethepercentageofcases.Forexample,ifyouhadamillioncasesandthereare50casesthathavethesame"setoffindings",youcanwrite10%intherowthatmatchesthatdataset.Thisindicatesthatyouhaveseen10%ofcaseswiththeseexactfindings.Neticawillthenrunthatlinethrough10times(orwhateverrepresents10%ofthecases).

Link:TheWindowsdatabasesoftwaremustbeabletoidentifytheExcelworksheetasadatabasetable.Itmaydothisautomatically,orfromExcelyoumayhavetoselectalltherelevantcells,andtheninthelittleboxtotheleftoftheformulabar(fordefiningnames),enterinanynameandpressENTER.Finally,savethefile.Note:ifyouareusingNeticaonaMac,itwillthrowanerrorwhenlearningfromanExcelfile.Youmustconvertyourdataintoatextfileinorderforthelearningtowork.

SubsetofCells/ChoosingTable:Ifyoualreadyhaveseveraltablesdefinedin

thespreadsheet,oryouwantNeticatojustuseasubsetofthecells,selectthesetofcellsyouwanttouse,anddefineitwiththename“ForNetica”,asdescribedabove.Wheneverthereisatablewiththatname,Neticawilluseitinsteadofanyother.

>>NextStep

LearningFromCasesUsingExcel1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

YoumayalreadybestartingwithaBayesnetthathasnodeswithsuitablenamesandstatestomatchtheExceldata,inwhichcaseyoucangoontothenextstep.Ifnot,youwillhavetoaddnodesorchangetheirnames,asdescribedbelow,orletNeticadoitautomaticallyasdescribedfurtherbelow.

Manually:Ensurethateachnode'snameoritstitleexactlymatchesthetextinthecellatthetoprowoftheExcelspreadsheet.Also,thestatenamesortitlesmustexactlymatcheachofthepossibleentriesinthatcolumn(unlessthecolumncontainsnumericdata).Thematchesarecasesensitive.

Toachievethis,youmaywanttochangethenamesofthenodes,orchangetheExcelcells,oraddnodetitles.

Important:IftheExcelnameshavespacesorspecialcharactersinthem,theywon'tbeabletomatchthenodeorstatenames(sincethosecharactersarenotallowedinnames),sotheywillhavetomatchnodeorstatetitles.

Automatically:AgreattimesaverisNetica’sabilitytoexaminethespreadsheetandaddnodestotheBayesnetwithproperlymatchingnodeandstatenames.TheBayesnetmaystartoffempty,oritmayalreadyhavesomenodes.ChooseCases→Learn→AddCaseFileNodes,andfromtheopen-filedialogboxpresented,choosetheExcelfilewiththespreadsheet.Afterthenodesareadded,youmaywanttore-arrangetheirposition,ordeleteonesyouaren’tinterestedin.Nodesfornumericdatawillbeaddedas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenodes,whichyouprobablywanttoconvertto=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousnodes,andthenextstepdescribesanautomaticwaytoeasilydothat.

ExtremelySlow:IfExcelisrunning,andhasopenthesamefilethatyouaretryingtoworkwithinNetica,theoperationsinNeticawillbeextremelyslow,soclosethefileinExcelfirst.

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LearningFromCasesUsingExcel1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

Youneedto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizecontinuousnodes,andiftheyhavealreadybeendiscretized,youmaywanttoadjustthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_threshold.htm');returnfalse;">thresholdstobettercapturetheExceldata.Ifthenodeswereaddedautomatically,thenyoumaywanttoconvertdiscretenumericnodestocontinuousones,andthendiscretizethem.

Automatically:TousehistograminformationgeneratedfromtheExceldataset,selectoneormorenodesandchooseModify→DiscretizeNodefromthemenu.Anyofthenodesthatare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretewillbeconvertedto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuous.Neticamayaskyouwhatfileyouwishtousetogeneratethehistogram,towhichyouwouldnormallyindicatetheExcelspreadsheetfile.ThenNeticawillaskhowmanystates(i.e.bins)youwanteachnodetohave,andthedegreeofrounding(20%isusuallyagoodamount).Finally,itwillautomaticallydothediscretizationsothatthebinshaveapproximatelyequalamountsofdatasamples.Ifyouspecified0%fortherounding,theneachbinwillhaveascloseaspossibletothesamenumberofsamples,andifyouchose

alargernumber,thebinamountswon’tbeexactlyequalsinceNeticatriestochoosesomewhatroundnumbersforthethresholds.

Manually:Alternatively,youcanmanuallychangediscretenodestocontinuouswiththenodepropertiesdialog,andforcontinuousnodes,youcandiscretizethemoradjusttheirdiscretizationthresholdswiththeNodeDiscretizationsetter.

CombineStates:Iftheentriesinacolumnarenotnumeric,andtherearesomethatyoudon’tcareabout,youcanDELETEthenode’sstateswhichcorrespondtothem,andthenaddastatecalledother.

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LearningFromCasesUsingExcel1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

Oncetheappropriatenodesareinplaceandtheirdiscretizationlevelschosen,addthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructurethatyouwanttoworkwith.Youcandothismanuallyasdescribedbelow,oryoucanuseTANLearning.

Ifthereisonevariableofinterestthatismostimportant(calledthe“targetvariable”or“targetnode”),thenitisbesttodrawlinksfromittoalltheothernodes.Thatwayyouaredirectlycapturingitssinglerelationshipwitheachoftheothernodes.

Rememberthateachnodeshouldnothavetoomanylinksenteringit,sincethenits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTtablewillbetoolarge,andtherewillnotbeenoughsamplinginformationinthespreadsheettoadequatelyfillallthecells.

Thereisnoprobleminhavingagreatmanylinksleavinganode,andsinceNeticawilldoBayesian=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">inferenceontheresults,itisokayforlinkstogoineitherdirection.Thatiswhytoclassify,predictordiagnosisaparticularvariablewiththebestaccuracy,youwanttocaptureitsrelationwithasmanyoftheothervariablesaspossible,soyouputmanylinksleavingthatvariable.

Iftheonlylinksthatarepresentinthenetareonesthatleavethetargetnode,thenalthoughthewaythateachothernodeeffectsthetargetnodehasbeencaptured,theyareonlybeingconsideredinisolation,andsynergisticeffectsofthewayinwhichtheyeffectthetargetnodearebeinglost.

Example:Saythatwewanttocapturethesynergybetweenthe3strongestinfluencersofthetargetnode.Wemightuse“SensitivitytoFindings”(seefurtherbelow)toidentifythese3nodes.Thenwecanputlinksfromthose3nodesintothetargetnode,andfromthetargetnodetoalltheothernodes.Ineffectthatsays,“Considerindetailthesynergybetweenthe3mostimportantinfluencersofthetargetnode,andfortherestofthenodes,considerallofthem,butnotallthesynergiesbetweenthem.”

UsingInference:SinceNeticadoesBayesianinference,thereisanalternatewaytoaccomplishtheabove,thatisn’timmediatelyintuitive.Wecanhavelinksgoingfromthetargetnodetoeachoftheothernodes,andthenjustputlinksbetweenthestrongestinfluencers.Thismethodwillproducethesameresults,anditispreferable,sinceitmakesexploringanumberofmodelseasier.Also,itallowslinkingtwovariableswhosesynergisticeffectswewanttoexplore,andlinkinganothertwosuchvariables,andyetstillconsideringthetwopairsasindependentlyinfluencingthetargetvariable.

Sometimesyouwanttoputlinkssimplytocreatea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTwithcertainparentnodes,sothatyoucanlaterobservetheconditionalprobabilitiesinthattable.

Ifyouwanttotakeadvantageofdomainindependenceinformation,oryouaredevelopingacausalmodel,thatmayalsoinfluencethedirectionoflinksyouchoose.However,keepinminditispossibletolearntheCPTsusingonelinkstructure,thenlaterreverseanddeletelinkstocapturethecausaldirectionsyouwant,asdescribedfurtherinthissection.

Ingeneral,therearemanypossibilitiesforgoodlinkstructures,dependingonwhatyouwanttoaccomplish.Youmaywanttoexperimentwithafewdifferentstructures,toseetheresultsyougetfromeach.Forexample,youcanuseNeticatodostructurelearningbywritingyourownsmallprogramthattestsanumberofcandidatelinkstructurestofindthebestone.Youwritea

functionwhichsearchesthroughsomecandidatelinkstructuresthatareplausibleandpracticalinyourdomain,perhapsalsoaddingtriallatentvariables.ForeachstructureyouuseNetica’sparameterlearningfunctionsdescribedinlearningfromcases,thentesttheresultingnetwithNetica’snettestingfunctionsalsodescribedinthischapter.Thenetthatscoresthehighest(perhapspenalizedforcomplexity)isthebeststructure.

AddLinksFast:Todrawlinksfromonenodetoawholesetofnodes,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthesetofnodes,thendrawasinglelinkfromthedesiredparentnodetooneoftheselectednodes,andNeticawilladdallthelinks.

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LearningFromCasesUsingExcel1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

ThenextstepistohaveNeticalearntheconditionalprobabilitytables,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTs.

ChooseCases→Learn→IncorpCaseFilefromthemenu,andfromtheopen-filedialogboxpresented,choosetheExcelfilewiththespreadsheet.Whenasked,entera“degree”of1.0unlessyouarelearningfrommorethanonedatasource,andyouwanttoweighteachone.NeticawillprocesstheExcelspreadsheet,andfilleachnode’sconditionalprobabilitytable.

Note:Whenlearningfromdatasets,thetoprowdoesnotnecessarilyneedtohavethenodename(Neticacanstilllearnthedataifthereisn'tarowheading/nodename).Itispreferabletohaveanodename,butNeticacanlearnitwithoutthename.Ifitdoeshaveanodename,itmustexactlymatchandmustnotcontainspacesorspecialcharacters.Seecasefileformatformoreinfo.

Ifthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowisvisible,youwillbeabletoseetheprogressasthepercentofcasesprocessedsofar.YoucanaborttheoperationbypressingCTRLwhileholdingdownthemousebuttonforawhile.

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LearningFromCasesUsingExcel1.CreateanExcelSpreadsheet2.AddNodestotheNet3.DiscretizeorCombineStates4.AddLinkStructure5.LearnCPTs6.UsetheResultingBayesNet

OncetheCPTshavebeenlearned,youcanusetheresultingBayesnet.Ifnecessary,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compilethenettodo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">probabilisticinferencebychoosingNetwork→Compile,orclickthetoolbarbutton.Youcandowhat-ifanalysisbyentering=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsforsomenodes(byclickingonthestatenames),andobservinghowalltheprobabilitieschange.

Ifyouhaveaparticularnewcaseyouwishtoanalyze,thenyoucanentereverythingyouknowaboutitasfindings,andthenobservetheresultingprobabilitiesofthetargetnodetohaveNeticadoclassification,predictionordiagnosis.

Youcanopeneachnode’s=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTdialogboxtoviewtheconditionalprobabilitiesofeachnodegivenitsparentnodes.

Ifthereisonevariableofparticularinterest(the“targetvariable”),thenyoucanseehowstronglyeachoftheothervariablesarerelatedtoitbyselectingitandchoosingNetwork→SensitivitytoFindingsfromthemenu.To

understandthereportgenerated,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">contactNorsysfortheSensitivitydocument.

YoucancopyandpastepartsofthenetworkintoanothernetworktocombineknowledgelearnedfromthisExcelspreadsheetwiththeknowledgefromtheothernetwork(whichmayhavebeenlearnedfromotherdata,orcreatedbyhandbyanexpert).Ifyoudothis,youmaywanttouseModify→ReverseLinksanddeletesomeextraneouslinksbeforeyoucopyandpaste,togetthelinkdirectionsintheright(i.e.causal)directionfirst.

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ExperienceTherehasbeenconsiderablecontroversyoverthebestwaytorepresentuncertainty,withsomeofthesuggestionsbeing:probability,fuzzylogic,nonmonotoniclogic,belieffunctions,Dempster-Shafer,etc.Currentlyprobabilityandfuzzylogicarethemostpracticalmethodsformostapplications.Ofthesetwo,probabilityhasamuchsoundertheoreticalbasis(atleastwithrespecttothewaytheyareactuallyused).However,probabilitybyitselfdoesnotrepresenttheconfidenceonehasinone'sbeliefs,orlackthereof(e.g."ignorance")

Example:Supposeyouhadtodrawaballfromabagfullofblackandwhiteballs,andyoucouldn’tobservehowmanywhiteballsorblackballsareinthebag.Ifyouhadtosupplyaprobabilitythatyouweregoingtodrawawhiteball,itshouldbe0.5,providingyouhadnoadditionalinformation.

Contrastthatwithasituationinwhichyoucancounttheballsinthebagbeforehand(thereare10ofeach),andyouwillshakethebagbeforeyoudraw.Inthissituationtheprobabilityofdrawingawhiteballis0.5,butwhereasinthefirstsituationyouwereinastateofignorance,nowyoufeelmuchmoreinformed.

Ifyouneededtodo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">probabilisticinferenceorsolvedecisionproblems,thenthe0.5probabilitywouldbesufficientineithersituation.Inbothsituationsyoushouldbelieveandactasiftherewasanequalchanceofdrawingawhiteorablackball.Sotheconceptofexperienceisnotrequiredforthesetypesofproblems,andyoudonotneedtobeabletorepresentignorance(ignoranceistheendpointoftheexperiencespectrum).However,forlearningandcommunicatingknowledge,itisusefultobeabletorepresentthedegreeofexperienceaswellastheprobability,asweshallsee.

Supposeyouthensequentiallydrawanumberofballsfromthebag.Ifyoudrew3whiteballsinarow,theninthefirstsituationyourprobabilitythatthenextballwillbewhiteshouldbegreaterthan0.5,becauseyouarelearning(perhapsincorrectly)thatthereseemtobealotofwhiteballs.Inthesecondsituationyourprobabilityofthenextballbeingwhiteshouldbelessthan0.5,

becauseyouknowthatnowtherearemoreblackthanwhiteballsleftinthebag.Sinceyoushouldarriveatdifferentconclusionsineachofthetwosituations,youneedsomemoredetailedwayofrepresentingtheoriginalknowledgethanjustP(white)=0.5.

Onewaytohandlethisusingjustprobabilitiesistokeeptrackofyourbeliefsabouttheratioofwhitetoblackballsinthebag.Thenyouwillhavemanyprobabilities,oneforeachpossibleratio.Eachoftheseprobabilitieswillchangeasyoudrawaball,andwhenyouareaskedtosupplyaprobabilitythatthenextballdrawnwillbewhite,theywillallbeinvolvedinthecalculation.Thesearesometimescalledsecondorderprobabilities,butinthisexampletheyarereallyjustaprobabilitydistributionoverpossibleratiosofballs.ItwouldbeeasytocreateaBayesnetforthis,whichwouldhaveanextracontinuousnoderepresentingtheactualratioofballsinthebag,andbeliefsforeachpossibleratiowouldbeupdatedwitheachobservation(foranexampleofthis,seethe"BetaUpdating"net).Thatapproachworksfineforthissimpleproblem,butyoucanimaginethatifyouhadmanyinterrelatedvariables,thatitwouldbecometoocomplicated,becauseyouwouldneedaseparateextranodeforeachprobabilitynumberofeach=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPToftheoriginalnet.

InsteadNeticausestheconceptofexperience,whichisameasureoftheconfidencethatNeticahasinitsprobabilities.

AteachnodeNeticakeepsanexperiencetable,whichhasasingleexperiencenumberforeachrowoftheCPT.Theexperiencevaluecorrespondscloselytothenumberofcasesthathavebeenseenoritsequivalent(normallyitis1morethanthenumberofcases).Thisformofexperiencehassometimesbeencalledthe“equivalentsamplesize”or“ess”.Tosavespace,Neticadoesn’tkeepexperiencetablesfornodesthathaven’tbeeninvolvedinanylearningandhaven’thadamanualentryofexperience.Youcanvieworeditexperiencetableswiththetableeditor.

Theexperiencenumbersarenotinvolvedinprobabilisticinferenceordecisionproblems,sincetheyaren’tneededthen.ButwheneverNeticadoeslearning,theyareinvolved(andthatwilleffecttheCPTs,whichwilleffectfuture

probabilisticinferenceanddecisionproblemresults).(Moreinfoonhowexperienceiscalculated)

Counting-LearningAlgorithmThisdescribesthesimplestalgorithmusedbyNeticaforparameterlearningofconditionalprobabilitytables(CPTs)fromafileofcases,calledcounting-learning.Althoughitissimple,itisatrueBayesianlearningalgorithm.

Beforelearningbegins,thenetstartsoffinastateofignorance(providingtherehasbeennopreviouslearningorentryofprobabilitiesbyanexpert).Ateachnode,all=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTprobabilitiesstartasuniform,andeachexperiencestartsatitslowestvalue(normally1.0).

Foreachcasetobelearnedthefollowingisdone.Onlynodesforwhichthecasesuppliesavalue(finding),andsuppliesvaluesforallofitsparents,havetheirexperienceandconditionalprobabilitiesmodified(i.e.,no=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_missing_data.htm');returnfalse;">missingdataforthatnode).Eachofthesenodesismodifiedasfollows.

Onlythesingleexperiencenumber,andthesingleprobabilityvector,fortheparentconfigurationwhichisconsistentwiththecaseismodified.Thenewexperiencenumber(exper')isfoundfromtheold(exper)by:

exper'=exper+degree

wheredegreeisthemultiplicityofthecase(setbyyoujustbeforelearningbegins).Itisnormally1,butisincludedsothatyoucanmakeit2tolearntwoidenticalcasesatonce,or-1to“unlearn”acase,etc.IfthecasefilehasaNumCasescolumn,thenactuallydegreewouldbetheproductofthedegreeyouenteredandthevaluefromtheNumCasescolumn.

Withintheprobabilityvector,theprobabilityforthenodestatethatisconsistentwiththecaseischangedfromprobctoprobc'asfollows:

probc'=(probc*exper+degree)/exper'Theotherprobabilitiesinthatvectorarechangedby:

probi'=(probi*exper)/exper'whichwillkeepthevectornormalized(experandexper'actastheoldandnewnormalizationconstants).

BayesianLearningGenerallyspeaking,itisawiseideatorelateanyproposedmachinelearningmethodtoaBayesianmethodtobetterunderstanditsassumptions,strengthsandweaknesses.Ifitcanbecast,atleastapproximately,intoaformofBayesianlearning,thenyoucanchecktoseeifthepriorprobabilitiesaresuitablefortheproblem.IfitdoesnotevenroughlycorrespondtoanyformofBayesianlearning,thenthereislittleguaranteeinthevalidityofitsresults,anditshouldonlybeusedifithasothervaluablequalities,suchasbeingparticularlysimpleorfast.

TheNeticalearningalgorithmisequivalenttoasystemoftrueBayesianlearning,undertheassumptionsthattheconditionalprobabilitiesbeinglearnedareindependentofeachother,andthepriordistributionsareDirichletfunctions(ifanodehas2states,theseare“betafunctions”).FormoreinformationseeSpiegelhalter&DLC93,section4.1(withtheword“precision”equivalenttoour“experience”).

AssumingthepriordistributionstobeDirichletgenerallydoesnotresultinasignificantlossofaccuracy,sinceprecisepriorsaren’tusuallyavailable,andDirichletfunctionscanfairlyflexiblyfitawidevarietyofsimplefunctions.Assumingtheconditionalprobabilitiestobeindependentgenerallyresultsinpoorperformancewhenthenumberofusablecasesisn’tlargecomparedtothenumberof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentconfigurationsofeachnodetobelearned.

FadingWhenaBayesnetissupposedtocapturerelationshipsbetweenvariablesinaworldwhichisconstantlychanging,itisusefultotreatmorerecentcaseswithahigherweightthanolderones.AnexamplemightbeanadaptiveBayesnetthatisconstantlyreceivingnewcasesanddoinginferenceswhileitslowlychangestomatchachangingworld.

Neticaachievesthispartialforgettingofthepastbyusingfading.Youdoregularlearningfromcasesasthecasesarrive,andeverysooftenyouselectthenodestobefaded,chooseTable→Fade,andenteradegreefrom0to1.Neticawillreducetheexperienceandsmooththeprobabilitiesoftheselectednodesbyanamountdictatedbythedegree,with0havingnoeffect,and1creatinguniformdistributionswithnoexperience(therebyundoingallpreviouslearning).Thenwhenyoucontinuetolearnnewcases,theywilleffectivelybeweightedmorethanthecasesyoujustfaded.

Fadingoncewithdegree=1d,andagainwithdegree=1f,isequivalenttoasinglefadingwithdegree=1df.Sotheeffectsofmultiplefadingsaccumulateastheyshould.Tobemostaccurateyouwouldfadeaverysmallamountaftereachcase,butforallpracticalpurposesyoucanjustfadealargeramountafterabatchofcases.

Ifanoccurrencetimeforeachcaseisknown,andthecasesarelearnedsequentiallythroughtime,thentheamountoffadingtobedoneis:degree=1–r^ twhere tistheamountoftimesincethelastfadingwasdone,andrisapositivenumberlessthan(butcloseto)1,anddependsontheunitsoftimeandhowquicklytheenvironmentischanging.Differentnodesmayrequiredifferentvaluesofr.

Duringfading,eachoftheprobabilitiesinthenode’sconditionalprobabilitytable(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPT)ismodifiedasfollows(whereprobandexperaretheoldvaluesofprobabilityandexperience,andprob'andexper'arethenewvalues):

prob'=normalize(prob*exper*(1-degree)+degree)

exper’isobtainedasthenormalizationfactorfromabove(rememberthatthereisoneexperiencenumberpervectorofprobabilities).So:

prob'*exper'=prob*exper*(1-degree)+degree

StructureLearningWearecontinuallyaddingtoNetica'slearning-from-datacapability(structure,parameter,testing).ThefirstadditionistheTANStructurelearningofversion5.00.TANstructurelearningistheautomaticmethodforlearningthelinkstructureofaBayesnetfromacasefile.

Howto:First,selectatargetnodethatyouwanttodiagnose/predict.Next,chooseCases→Learn→LearnTANStructure.Neticawillautomaticallydeterminetheappropriatelinkstructure.

Asnotedinthetopiclearningthelinkstructure,thereisnoprobleminhavingagreatmanylinksleavinganode,andsinceNeticawilldoBayesian=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">inferenceontheresults,itisokayforlinkstogoineitherdirection.Thatiswhytoclassify,predictordiagnosisaparticularvariablewiththebestaccuracy,youwanttocaptureitsrelationwithasmanyoftheothervariablesaspossible,soyouputmanylinksleavingthatvariable.

Furtherdocumentationwillbeavailableshortly;inthemeantime,youcanreadFriedman,Niretal1997todiscoverhowNeticadoesTANlearning(freeversionavailableonlineorbye-mailingus).

Ifyouhavesomedatasetsthatyouwouldlikeustousethroughoutourresearchwewouldbehappytousethemandsendyoualltheresults.

DecisionNetsDecisionnetsareusefulinsolvingdecisionproblems,wheretheinterrelationsbetweenvariablesarerepresentedasina=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnet,andthegoalistofindasetofdecisionfunctionswhichmaximizeautilityobjective.Anexampledecisionnetis“Umbrella”.

CreatingadecisionnetissimilartocreatingaBayesnet.Oncethedecisionnetisconstructed,itmaybesolved,afterwhichyoumaywanttodomodel-iterationandwhat-ifanalysis.

DecisionNetsBayesnetsareusedtodeterminenewbeliefs(intheformofprobabilities)asobservationsaremadeorfactsaregathered.Theyarecomposedonlyofnaturenodes.Toformadecisionnet(alsoknownasan“influencediagram”),youadddecisionnodesandutilitynodes(alsoknownas“value”nodes).Decisionnodes,whicharetraditionallydrawnasrectangularboxes,correspondtovariablesoreventsthatyouwillbeabletocontrol.Utilitynodesaredrawnwithadiamondorflattenedhexagonshape,andcorrespondtoquantitiesyouwanttomaximize.

Thedecisionnetasawholerepresentsadecisionorplanningproblemthatyouface,orthatsomeotheragent,oftencalled“thedecisionmaker”,faces.Neticacanfindvaluesforthedecisionnodesthatwillresultinthelargestpossibleexpectedvaluefortheutilitynode(orsumofthemifthereismorethanone).Thisisknownas“solving”thedecisionnet.Oncethenetissolved,you(orthedecisionmaker)canbegintoenacttheplanbytakingtheprescribedactionforeachdecisionasitarises.

Linksthatgointoadecisionnodehaveaspecialmeaningandarecalledinformationallinks.Theyindicatewhatwillbeknownatthetimethedecisionistobemade.Thatis,thedecisionmakerwillknowthevaluesofallthenodeswhichhavelinksintothatdecisionnode,andwillnotknowthevaluesofanyothernodes.

EarlieritwasstatedthatwhensolvingadecisionnetNeticafindsvaluesforeachofthedecisionnodes.Butiftherearesomelinksenteringadecisionnode,itactuallyfindsadecisionvalueforeachpossibleconfigurationofvaluesofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parents.Thisisacontingentplan,withaformlike:“ifIobserveA=highandB=no,thenIwilldoX,ifIobserveA=lowandB=yes,thenIwilldoY,andsoon.So,solvinganetfindsadecisionfunctionforeachdecisionnode(i.e.afunctionwhichgivesadecisionvalueforeachpossiblesetofparentvalues).

Ifthereareanumberofdecisionnodes,possiblycorrespondingtodecisionsmadeatdifferentpointsintime,thensolvingthenetwillfindadecisionfunctionforeachofthem,andthissetofdecisionfunctionsisknownasa

policy.Itisafullconditionalplan,specifyingwhattodoineachpossiblecontingency,basedontheinformationthatwillbeavailable.

Workingthroughanexamplemaymaketheseideasclearer,andthenyoumaywanttocreateyourown.

“Umbrella”ExampleDecisionNetAverytinydecisionnetfromRossShachterknownas“Umbrella”servesasagoodsimpleexample.YoucanreaditintoNeticafromthe“Examples”folder.

Ithas2naturenodesrepresentingtheweatherforecastinthemorning(sunny,cloudyorrainy),andwhetherornotitactuallyrainsduringtheday(rainorno_rain).Ithasadecisionnodeofwhetherornottotakeanumbrella,andautilitynodethatmeasuresthedecisionmaker’slevelofsatisfaction.ThereisalinkfromWeathertoForecastcapturingthebelievedcorrelationbetweenthetwo(perhapsbasedonpreviousobservations).

ThereisalinkfromForecasttoUmbrellaindicatingthatthedecisionmakerwillknowtheforecastwhenhemakesthedecision,butnolinkfromWeathertoUmbrella;ifheknewforcertainwhattheweatherwasgoingtobe,itwouldbeeasytodecidewhetherornottotaketheumbrella.

TherearelinksfromWeatherandUmbrellatoSatisfaction,capturingtheideathatheismosthappywhenitissunnyandhedoesn’ttakeanumbrella(utility=100),nextmostwhenitisrainingandhetakesanumbrella(utility=70).Hehatescarryinganumbrellaonasunnyday(utility=20),butismostunhappyifitisrainingandhedoesn’thaveone(utility=0).Youcanexaminetheutilityvaluesby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingnodeSatisfaction,andthenclicking

Tocompilethisdecisionnet,click ..Auto-updatingisturnedonforthisdecisionnet,soassoonasyoucompileit,updatingwilloccur(i.e.itwillbe“solved”).

Thedisplaywillchangetosomethinglike:

Thenumberbesideeachdecisionchoiceindicatestheexpectedutilityofmakingthatchoice.Sobeforeanyinformationisknown,decidingtotaketheumbrellaresultsinanexpectedvalueof35,whileleavingitathomegives70.Clearlythebestchoicegiventheavailableinformationistoleavetheumbrellaathome.

Ifthedecisionmakerhearsthattheweatherforecastissunny,thenthiscanbeenteredbyclickingontheword“sunny”oftheForecastnode.Theexpectedutilitiescorrespondingtoeachdecisionchoicechange.Thebestdecisionisstilltoleavetheumbrellaathome,buttheexpectedutilityhasincreasedto91.59,becausetheextrainformationindicatesitisnowmorelikelythattheumbrellawon’tbeneeded.

Sayinsteadtheforecastwascloudy.Clickontheword“cloudy”tochangethefinding.Stillthebestdecisionistoleavetheumbrellaathome,buttheexpectedutilityhasdecreasedto65.12,becauseoftheincreasedchanceofrain.

Tryaforecastofrainy.Thebestdecisionchangesto“taketheumbrella”,andtheexpectedutilityofthatdecisionis56.

Withnofindings=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredfornodeForecast(sinceitistheparentnode),selectnode“DecideUmbrella”,andclickon .Thetabledialogwillopen,andthereyoucanseetheoptimaldecisionfunction,whichistoleaveitathomeunlesstheforecastisrainy.

ForamoreadvancedexampleseeCarBuyer.Itrepresentsasequentialdecisionproblem(hasalaterdecisiondependingonthefirst),andithasmultipleutilitynodes.

“CarBuyer”ExampleDecisionNet“CarBuyer”isanexampledecisionnetillustratingsequentialdecisionsandmultipleutilitynodes.Foramoresimpleexample,seetheUmbrellaexample.

Open“CarBuyerNeapolitan”fromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder.ItisfromNeapolitan90,whichisasimplerversionofthecarbuyerexampleofHoward62.Eliminatingtherationalegiventhereofhowthenumbersarearrivedat,wehavethefollowingstory:

Joeisgoingtobuyausedcar,whichcouldbegoodwithprobability0.8oralemonwithprobability0.2.Afteraccountingforrepairs,Joe’sprofitwillbe$60ifthecarisgood,and$-100ifitisbad.Beforebuyingthecarhehastheoptionofhavingonetestortwotestsdoneonit.Thefirsttestcosts$9,andbothtogethercost$13.Thefirsttesthasa90%chanceofreturningpositiveifthecarisgood,anda40%chanceifit’salemon.Ifthefirsttestreturnspositive,thenthesecondtesthasa88.89%chanceofreturningpositiveifthecarisgood,anda33.33%chanceifit’salemon.Ifthefirsttestreturnsnegative,thenthesecondtesthasa100%chanceofreturningpositiveifthecarisgood,anda44.44%chanceifit’salemon.

Joehas2decisionstomake:whethertodothetests,andwhethertobuythecar.Thesearerepresentedbythe“DoTests?”and“BuyIt?”decisionnodes.Theoutcomeofthetestsaregivenbynodes“FirstTest”and“SecondTest”.ThecostsofthetestsarerepresentedbyutilitynodeU,andtheprofitsafterrepairs(notincludingtestcosts)byutilitynodeV.Theoverallutilityisthesumofthesetwo(withcostsbeingnegative).

WhenJoedecideswhethertodothetests,hedoesn’tknowthevalueofanyofthesevariables,sotherearenolinksenteringthe“DoTests?”node.Whenhedecideswhethertobuy,hewillknowtheoutcomeofbothtests(theoutcomesmaybe“notdone”),andsotherearelinksfromthosetwonodesto“BuyIt?”.Hewillalsoknowthevalueof“DoTests?”sincehehasalreadymadethatdecision,soyoucouldputalinkfromthatnodeto“BuyIt?”,butitisnotnecessarysinceitisano-forgettinglinkandthereisalreadyadirectedpathfrom“DoTests?”to“BuyIt?”.

Youcanexaminetherestofthelinkstructure,andcheckouttherelationtables,tomakesuretheymakesensetoyou.

Thencompilethenet.Sinceauto-updatingisturnedon,itwillbesolvedimmediately.Neticaaddsano-forgettinglinkfrom“DoTests?”to“BuyIt?”,indicatingthat“DoTests?”mayberelevanttotheseconddecision,basedonlyontherestofthelinkstructure(asitturnsout,itisn’t).Theexpectedutilityofeachdecisionchoicefor“DoTests?”isprintedinthenode;notdoinganyofthetestshasthehighestexpectedutilityof28,soitisthebestchoice.Noexpectedutilitiesareprintedinthe“BuyIt?”node,sincethefirstdecisionhasnotyetbeenmade.

Ifyouclickonthe“None”decisionof“DoTests?”toindicatethatJoedecidesnottodoanytests,expectedutilitiesappearinthe“BuyIt?”node.Thebestchoiceistobuyit,resultinginthehighestexpectedutility–anoverallprofitof$28.Tryclickingon“First”ofthe“DoTests?”nodes,indicatingthatJoedecidestojustgetthefirsttestdone.Hisoverallexpectedutilityis26.2.Thenclickindicatingthatthefirsttestoutcomewas“Positive”.Thebestdecisionistobuyandtheexpectedutilityis35.Ifthefirsttestcomesoutnegative,thenthebestdecisionistonotbuy,anditsexpectedutilityis–9(whichisthecostofthetest).Youcanexperimentwithothercombinationsoffindingsanddecisionchoices.

Nowperhapsyouwanttocreateyourowndecisionnet?

CreatingaDecisionNetCreatingadecisionnetisprettymuchthesameascreatingaBayesnet,soitinvolvesaddingthenodesandlinks,settingnodepropertiesandenteringnodetables.

Onedifference,obviously,isthatyoumustdesignatesomenodesas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynodes.Usuallyyoudothiswhenyoufirstaddthem,byusingthe toolbarbuttontoadddecisionnodes,andthe buttontoaddutilitynodes.However,youcanchangenodekindsusingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogbox,orbyselectingthenodesyouwishtochange,andthenclickingonthetoolbarbuttonforthedesiredkind,whileholdingdowntheCTRLkey.

Youdon’tentera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">tablefordecisionnodes,sinceNeticafindsthatwhenitsolvesthedecisionnet.

Utilitynodesmustbecontinuous,anddonotneedtobediscretized.Youmayhavemultipleutilitynodes,andNeticawillusethesumofthemasthetotalutility.Utilitynodesshouldnothave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">children.

Thereshouldbeatleastone=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_path.htm');returnfalse;">directedpaththroughallthedecisionnodestoindicatetheirorderingintime.Youdonotneedtoaddno-forgettinglinks;Neticawilladdanynecessaryoneswhilesolvingthedecisionnet.

No-ForgettingLinksNormally,intheprocessofmakingadecision,adecision-makerwillknowatleasteverythingknownforearlierdecisions,aswellaswhatthoseearlierdecisionswere.

Thatcanberepresentedinthedecisionnetbyincludinglinkstoadecisionnodefromallearlierdecisionnodes,andfromalltheir=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentnodes.Theselinksarecalledno-forgettinglinks,sincetheyindicatethatalltheinformationthedecisionmakerknewearlier,hestillknowswhenmakinglaterdecisions.Keepinmindthatlinksenteringadecisionnodeare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_informational_link.htm');returnfalse;">informationallinks,andindicatewhatthedecisionmakerwillknowwhenhemakesthedecision.

Havingmoreinformationtomakedecisionsalwaysleadstoapolicyhavinggreaterexpectedutility,ifthatinformationisrelevant.Manyoftheno-forgettinglinksmaynotberelevant;theyprovideinformationaboutthepastthatdoesnothelpinthenewdecision.Iftheselinksareincluded,theoptimaldecisionfunctionswillsimplyignorethem,andtheexpectedvalueofthepolicywillbethesame,buttheymayresultinverylargerelationtablesforthelaterdecisions.

Whenconstructingadecisionnet,youdonotneedtoconcernyourselfwithno-forgettinglinks,aslongasyouputenoughtocreatea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_path.htm');returnfalse;">directedpathrunningthroughallthedecisionnodes(toindicatetheirtimesequence).WhenNeticasolvesthedecisionnetitwillremoveirrelevantno-forgettinglinks,andaddanyrelevantonesthatarenotpresent,basedonthestructureofthenet.

Ifyouwishtoseealltheno-forgettinglinksimpliedbyadecisionnet,makesurethereisa=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_path.htm');returnfalse;">directedpathrunningthroughallthedecisionnodesandchooseModify→AddNo-ForgettingLinks.Thisisusefulwhensolvingthedecisionnetusingthealternatemethodofnodeabsorption(insteadofcompiling).

SolvingaDecisionNetAftercreatingadecisionnet,youcancompileitinthesamewayasyoucompileaBayesnet(excepttheoptimizingcompilerdoesn’tworkondecisionnetsyet).

Neticawillattachtoeachdecisionnodeadeterministicfunction(theoptimalisneverprobabilistic),whichprovidesavalueforthedecisionnodeforeachpossibleconfigurationof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentvalues.Sincethelinksintoadecisionnodeindicatewhatthedecisionmakerwillknowwhenheisabouttomakethedecision,thisfunctionprovidesadecisionforeachpossibleinformationstate.Takentogether,thedecisionfunctionsfromeachofthedecisionnodesforma=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_policy.htm');returnfalse;">policywhichmaximizesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueofthesumoftheutilitynodes.Youcanusethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogboxtoexaminetheoptimaldecisiontableforeachdecisionnode.

Todisplaytheoverallexpectedutilitycorrespondingtoeachchoiceofadecisionnode,changethenodestyletobelief-bars.Thenumericalvaluewillappeardirectlyaftereachstatename(althoughnobarswillbedrawn).Thebestdecisionistheonewiththehighestexpectedutility.

FindingsanddecisionnodechoicesmaybeenteredinthesamewayasforBayesnets,andupdatingdonetorevealthenewprobabilitiesandexpectedutilities.

LinksChange:Whenyoucompileadecisionnet,Neticamayaddorremovesomelinksintodecisionnodes.Ifalinkdisappears,thenitmeansthatforallpossibleutilities,CPTsorfindings,thatlinkwon'tberelevanttothedecision.

Ifanewlinkappears,thenitisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_no_forgetting_link.htm');returnfalse;">no-forgettinglinkthatisrelevanttothedecision.

MissingNumbers:Ifthereisapathfromonedecisionnodetoanother,itmeansthattheancestordecisionistobemadebeforethedescendentdecision.Soyoumustenterachoicefortheancestordecisionnodebeforeutilitieswillbedisplayedatthedescendentdecisionnode(ifyouarefamiliarwithHugin,youwillknowthatitdisplaysutilitiesforthedescendentdecisionnodeallthetime,buttheHugindocumentationstatesthatthesevaluesarenotmeaningfuluntiltheancestordecisionchoiceisentered).

Example:Foranexampleofsolvingadecisionnet,seetheumbrellaexample.

SolvingaDecisionNetbyNodeAbsorptionUsuallyyousolveadecisionnetbycompiling,butifyouknowaboutnodeabsorption(linkreversal),youmaywanttousethat.Whensolvingbynodeabsorption,theremustbeonlyoneutilitynodeanditmustnothaveanychildren.Alsothenetmusthaveallno-forgettinglinksaddedbeforesolving.

ChooseNetwork OptimizeDecisions,andNeticawillattachtoeachdecisionnodeitsoptimaldecisionfunction.Takentogether,thedecisionfunctionsfromeachofthedecisionnodesforma=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_policy.htm');returnfalse;">policywhichmaximizesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueoftheutilitynode.Inthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">MessageswindowNeticawillprinttheexpectedutilityoffollowingthispolicy.Itwillalsoputupa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogboxshowingthedecisionfunctionforthefirstdecisionnode.Youcanusethenodeselectorintheupperlefttoseethedecisionfunctionsforothernodes.

Fortheumbrellaexample,thedecisionwillbe:

Forecast Bestdecision

sunny dont_take_umbrella

cloudy dont_take_umbrella

rainy take_umbrella

And“Expectedutility=77”willbeprintedintheMessageswindow.

Thenodeabsorptioncanalsobedonemanually.=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">Selectallthenodesandthenclickthe toolbarbutton.Thenetwillbedecomposedandonlythedecisionnodesandutilitynodewillbeleft.Eachdecisionnodewillhavetheoptimaldecisionasitsrelation,butitmayhavesomeparentlinksremoved.Anyremovedlinksareonesthatareirrelevanttothedecision.Alltheutilitynode’sparentswillberemoved,anditwillhavethemaximizedexpectedvalueasitstable.After=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">observingthetables(andperhapscopyingandpastingthemtoanewnet),youcanrestoretheoriginalnetbychoosingEdit Undo.

Alternatively,youcanabsorbthenodesone-by-one,butyoumustpickalegalorder(Neticawilltellyouifyoutrytouseawrongorder).

ModelIterationForsomeapplicationsofdecisionnets(especiallyinareaslikegambling,controlorautomateddecisionmaking),itisrelativelyeasytosetupthetablestosuitablyreflectreality,andthedecisionsthatthenetmakesaremuchbetterthandecisionsyouwouldmakeunaided,becauseofNetica’ssuperiorabilitytoreasonpreciselywithprobability,andtodealwithmanyinteractionsinverycomplexsituations.

Howeverforotherapplications(especiallyinareaslikebusinessdecisionmakingorpublicpolicy),thedecisionsthatNeticamakesmaynotmatchyour“gutfeelings”,andyoumaysuspectthatNeticaiswrong.Inthatcase,usuallythedecisionnetdoesn’tcapturethedecisionproblemwellenough.Theusualprocedureistogobacktothedecisionnetmodel,changeittomoreaccuratelyreflectreality,andsolveitagain.Thenrepeattheprocessuntilyouaresatisfiedwiththeresults.

But,ofwhatuseisthedecisionnetifallyoudoistrytogetittomatchthedecisionsyouwouldmakeanyway?Professionaldecisionanalystswhousedecisionnetsonaregularbasistellusthattheyareinvaluablefordisciplineddecisionmaking.Theprocessofbuildingthedecisionnetclarifiestheproblem(oftenslowlychangingyourgutfeelingasyouproceed),andtheiterationprocessforcesyoutore-examineassumptionsyouhavemade.

Inagroupdecisionmakingenvironment,creatingadecisionnetisoftenofgreatbenefitinfleshingoutthedifferencesinpeople’sbeliefsandvalues,andallowspeopletodiscussspecificsratherthanarguingingeneralities.

Also,oncethepolicyisformed,thedecisionnetactsasalivingdocumentofthebeliefsandvaluesthatleadtoit.Ifthosechangeovertime,thedecisionnetcanbechangedtogenerateanewpolicy.Orpartsofitcanbecopiedandpastedintonewnetsfornewdecisionproblems.Ifapolicyresultsinabadoutcome,itispossibletogobackanddeterminewhetheritwasbasedonbadinformation,andifso,tochangethatinformationforthenextdecisionmakingsituation.

What-ifDecisionAnalysisWithNetica’sundofeatureitiseasytosolveadecisionnet,undoit,changeautilityvalueoranodetable,andthenre-solvethenettoseehowtheoptimaldecisionsandmaximumexpectedutilityareaffected.

Butwhatifyouwanttoforceadecisionnodetohaveacertaindecisionfunction,andseehowtheotherdecisionsandmaximumexpectedutilitychange?Justenterthedesireddecisionfunctionforthenodeinitstabledialogbox(orpasteitin,sinceyouareoftenobtainingitfromaprevioussolutionofadecisionnet),selectthedecisionnode,andchangeitintoanaturenodebyclickingthe toolbarbuttonwhileholdingdowntheCTRLkey.Thensolvethenetintheusualway,andobservethechangestotheotherdecisionfunctionsandthechangetothemaximumexpectedutility.Ofcourseyoucanuse‘undo’toreturntotheoriginalsituation.Ingeneral,whenyouwanttosetadecisionnodetoacertaindecisionfunctionwhileyoucontinueyouranalysis,youtemporarilychangeitintoanaturenode.

DisplayStyleandPrintingTheStylemenuallowsyoutochangethewaynetsaredisplayedandprintedout,withoutchangingwhattheymeanorthewaytheybehave.Thesize,font,colorandlabelingofthenodescanbeadjusted,andindividualnodescanbedisplayedinaformwhichisbestforthatnode.Thelabelingandnatureofthedisplayedlinkscanalsobechanged.Themagnificationofthedrawingcanbeadjusted.

Netdiagramscanbeprintedwithaprinter,incolorandmagnified/reducedifdesired.PresentationqualitygraphicscanbecreatedbycopyingandpastingfromanetintootherapplicationsorbygeneratingSVGgraphics.

Ifanend-userwhoisnotfamiliarwithBayesnetsisgoingtobeusingthefinishednet,thenitcanbedisplayedinasuitablemanner,perhapsbyhidinglinksandsomenodes,anddisplayingtherestofthenodesasbargraphs,meters,ordataentryovals,dependingontheapplication.Youmayalsowanttoplacetextonthenetdiagram,toaddatitleornote.

NodeNameandTitleDisplayEverynodehasaname,butthereare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">restrictionsonnames.Toprovideyouwithgreaterflexibilityinlabelingnodes,someorallofthenodescanalsobegivenatitle,whichhasnorestrictions.Oneofthestyleoptionsofnodesishowthenameandtitlearedisplayedonthem.

Tohaveallthenodesofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenetdisplayedusingtheirname,chooseNamefromtheStylemenu,todisplaythembytitlechooseTitle,ortodisplaythemusingboth,chooseName:TitleorTitle(Name).Thechoicethatyoumakewillapplytoallthenodesofthenet,forbothscreendisplaysandprintingdisplays.

Tochangethenameortitleofanode,usethenodedialogbox.

Ifyouaredisplayingnodesbytitle,andsomenodesdon’thaveatitle,thentheirnamewillbeusedinstead.ThestartingstyleofanewnetisTitle,butyoumightnotnoticethisifyoudon’tenteranytitles,sincethenjustthenodenameswillappear.

FontandSizeOneofthestyleoptionsofnodesisthefontusedforthewritingwithinthem.Thenethasadefaultfont&sizefornodes,whichmaybechangedbymakingsurenonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,andthenchoosingStyle→Font(orby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchoosingModify→DefaultNodeStyle→Font).Adialogboxwillappearshowingthecurrentfontandsize,whichyoucanmodifyaccordingly.

Ifyou=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectsomenodesbeforedoingthisoperation,thenewfontwillapplytotheselectednodesonly,andwilloverridethedefault.

Ifyouchangethedefaultfont,andsomenodesdon’tchange,itisbecausetheyhaveanoverridingfont.Toresetthemtodefault,selectthem,right-clickontheselection,chooseStyle→Fontandsetthemtothesamefontasthedefault.

NodeSize:Wheneveryouchooseanewnodefont,oranewfontsize,thenodeswillberesizedsothatthewritingwithinthemfitsnicely.Infact,thewayyouenlargeorshrinkthenodesofanetistochoosealargerorsmallerfontsizeforthem.

Links:Tochangethefontforthelabelsofalldisconnectedlinks,useStyle→Links→LinkFont,oralternately,right-clickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">background

andchooseModify→DefaultLinkStyle.MoreInfo

CharacterSets:Keepinmindthatifyournetmustdisplayinternationalcharactersets,thenyoumustchoosea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Unicode.htm');returnfalse;">Unicodefontthatincludesthedesiredcharacters."ArialUnicodeMS"isusuallyasafechoice.

NodeColorOneofthestyleoptionsofanetisthecolorschemeofthenode-setswithinthenet.

DefaultNodeColors:

DecisionNodes:blue

NatureNodes:beige

UtilityNodes:pink

Note/TextNodes:lightblue

UndertheStylemenu,choose‘Colors’toproduceanode-setpropertiesdialogboxandarrangethenode-setcolorstoproducethedesiredvisualeffect.MoreInfo

NodeStylesThereareseveraldifferentformsinwhichanodecanbedisplayed,andtheseareknownasnodestyles.Thereisadefaultstyleforthewholenet,buteachnodecanbesettoitsownstyleindividually,whichoverridesthedefault.

DefaultStyle:Tosetthedefaultstyleforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenet,makesurethatnonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,andthenchoosethedesiredstylefromtheStylemenu,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchooseModify→DefaultNodeStyle.Ifsomenodesdon'tchange,perhapstheyhaveoverridingstyles(seebelow).

Tohavesomenodesoverridethedefaultstyle,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthemandthenchoosethedesiredstylefromtheStylemenu.Ifyouhavegivensomenodesanoverridingstyle,butnowyouwantthembacktothedefaultstyle,selectthemandchooseStyle→Default.

Forms:Thevariousnodeformsare:•Labeled-Box:

Drawsaboxwhoseshapeandcoloraredeterminedbythenodekind,withthename/titleofthenodewrittenwithinit(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicnodeswillbedisplayedusingathickborder).

•Belief-Bar: Drawsabargraphshowingthecurrentbeliefsforeachstateofthenode.

•Meter: Displaysaneedlemetershowingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_mean_value.htm');returnfalse;">meanvaluefor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousnodesandthecurrent=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">belieffor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenodes.

•Hidden: Doesn'tdrawanything(youcanalsohidethelinks).

•Circle: Displaysthenodeasasmallcircle.

OtherStyles:Keepinmindthatyoucanalsochangeotheraspectsofthenodestyle,suchasthesize,font,color,andlabelingofthenodes.

Belief BarNodeStyleThenodeformmostusefultodisplaythe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsofamulti-statenaturenode,orexpectedutilitiesofadecisionnode,isthebelief-barstyle.Nodescanbydisplayedinthisformby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingthem,andthenchoosingStyle→BeliefBars(choosethiswithnonodesselectedtosetthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_default_node_style.htm');returnfalse;">defaultstyleofthewhole=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activenet).

Eachnodewillbedisplayedasaboxlabeledatthetopwiththenode’sname,titleorbothdependingonthenode’slabeling.

Examplesofadiscretenode(left)andadiscretizedcontinuousnode(right):

Thenameofeachstateisshowninthesectiontotheleft,alongwithanumberexpressingthebelief(probability)ofthatstateasapercentage.Ifthenameistoolongtofit,itwillendwithan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_ellipsis.htm');returnfalse;">ellipsis.Ifthe

percentageistoosmalltodisplaynumerically,butnonzero,thenitwillbedisplayedas“0+”.

Scale:Inthesectiontotherightarebargraphsdepictingthebeliefamounts.Verticaldottedlinesmarkthe25%,50%and75%levels.Ifthenodehas4orlessstates,thentheleftedgeoftheboxis0%andtherightedgeis100%,butiftherearemorestates,thenthescalemaybeexpanded,sotherightedgeislessthan100%.Ifthescaleisexpandedsomuchthattherightedgeislessthan25%,thennoneoftheverticaldottedlineswillbevisible.

Finding:Ifthenethasbeensuccessfully=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compiled,a=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">findingmaybeenteredintoanodejustbyclickingonthenameofitsstate(andremovedbyclickingonitagain).A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativefindingforanodecanbeenteredbyholdingdowntheSHIFTkeyandclickingonthenameofthestatethatitsknownnottobe.

Ifthenodehasa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefinding,thenthebarforthestatecorrespondingtothefindingwillbeborderedaboveandbelowbyblacklinesandthenodecolorwilldarkentogray(unlessyou'vechangedthedefaultnodecolors).Ifthecolorofthenodeindicatesithasafinding,butnobarissurroundedbyblacklines,thena=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativeor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">likelihoodfindinghasbeenentered.

Mean&Variance:Ifanodeis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousorhas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">statevaluesdefined,thenits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_mean_value.htm');returnfalse;">meanvalue(i.e.,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalue)willbeshowninaseparateareabelowthebelief-bars.Themeanvaluewillbefollowedbya±symbolandits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_standard_deviation.htm');returnfalse;">standarddeviation.

DisplayFewerStates:ItispossibletohaveNeticadisplayonlythemostprobablestates,whichisveryusefulfornodeshavingmanystates.Ifyou=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectsomenodes,chooseStyle→ShowOnlyNStates,andenteranumber,thenthedisplayofthosenodeswillbelimitedtotheNmostprobablestates,orderedfrommostprobabletoleast.Atthebottomwillbeanentrycalled"other-"thatisthesumtotalofallthestatesnotdisplayed.Asyouenterfindingsandthebeliefschange,thenwhichstatesaremostprobablealsochange,sowhichstatesaredisplayed,andtheirordering,changes(ifyouwanttheirorderingpermanentlychangedbybeliefs,seehere).

IfnonodesareselectedwhenyouchooseShowOnlyNStatesfromthemenu,thenthenumberyouenterwillbethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_default_node_style.htm');returnfalse;">defaultforthewholenet.Nodesthathavefewerstatesthanthenumberyouenterwill

bedisplayednormally(i.e.withalltheirstatesintheorderyoudefined).Thedefaultforanetbeforeyouchangeitis50.Soifyounoticethatonly50statesarebeingdisplayedforthenodesinyournet,youcanusethismethodtochangethat.

Dimmed:Ifthebeliefpercentagesandbarlengthsarecurrentlyinvalidforthenet’sfindings(probablybecausethelatestfindingshavenotyetbeentakenintoaccountwitha=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating),thebarswillbedrawninagrayedordottedmanner.

MeterNodeStyle–DiscreteNodesMetersareoftenthenodeformofchoicefor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_binary_node.htm');returnfalse;">binarynodesliketrue/falsepropositionsorokay/faultyconditions.Example:

Belowthemeteristhenode’sname,titleorbothdependingonthenode’slabeling.Thetwostatesareprintedatthebottomofthemeter,ontheleftandright.Theneedleindicatestherelativebeliefineachstate.Fortheright-moststate,theleftendofthescalecorrespondstoabeliefprobabilityof0%andtherightendto100%.The50%pointiswhentheneedleisvertical,sothecenterofthescaleismarkedwithatick.

HowTo:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">SelectanydiscretenaturenodeandchooseStyle→Meter.IfnonodesareselectedwhenyouchooseStyle→Meter,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_default_node_style.htm');returnfalse;">defaultstyleforthewholenetwillbeset.Iftheneedlehasbandstothesides,ornumbersappearinsteadofstates(likethis),itisbecausethenodeiscontinuousorhas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">statevaluesdefined.

Finding:Ifa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingisentered,

thebackgroundcolorofthenodewillbechangedtogray(unlessyou'vechangedthedefaultnodecolors).Ifitisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefinding,theneedlewillbeallthewaytooneside,indicatingcertainty.

Dimmed:Ifthecurrentpositionoftheneedleisinvalidforthefindingsentered(probablybecausethelatestfindingshavenotyetbeentakenintoaccountwitha=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating),theneedlewillbedrawngray,ornotatall.

MoreStates:Ifthemeterstyleisusedforanodewithmorethantwostates,thenallthestatesexceptthefirstwillbegroupedtogetherandwillbecalled“Other”.Thefirststatewillberight-mostonthemeter,soitsbeliefwillbewellrepresentedbytheneedle(0%fullleftand100%fullright).

Continuous:Foracontinuousvariableexample,clickhere.

MeterNodeStyle–ContinuousNodesBelief-metersfornodesofcontinuousvariables,orthosewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">statevaluesdefined,displayaneedlewhichshowsthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueofthenode,andbandsonthesidesoftheneedlewhichshowthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_standard_deviation.htm');returnfalse;">standarddeviation,likethis:

Thenumbertotheleftofthescaleistheminimumvalueofthevariable,andtotherightisthemaximumvalue.Belowthemeteristhenode’sname,titleorbothdependingonthenode’slabeling.

HowTo:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">SelectanycontinuousnaturenodeandchooseStyle→Meter.IfnonodesareselectedwhenyouchooseStyle→Meter,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_default_node_style.htm');returnfalse;">defaultstyleforthewholenetwillbeset.Iftheneedlehasnobandstothesides,orstatenamesappearinsteadofnumbers(likethis),itisbecausethenodeisdiscrete.

Finding:Ifa=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingisentered,thebackgroundcolorofthenodewillbechangedtogray(unlessyou'vechangedthedefaultnodecolors).Ifitisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefinding,theneedlewillbeallthewaytooneside,indicatingcertainty.

Dimmed:Ifthecurrentpositionoftheneedleisinvalidforthefindingsentered(probablybecausethelatestfindingshavenotyetbeentakenintoaccountwitha=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating),theneedlewillbedrawngray,ornotatall.

Discrete:Foradiscretevariableexample,clickhere.

LinkStylesTheStyle→Linksmenuprovidesstyleoptions,whichallowyoutochoosethewayallthelinksinthenetaredisplayed.Themenuisalsoavailableby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchoosingModify→StyleDefaultLink.

Hidden:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">TogglingStyle→Links→HideLinksallowsyoutohideallthelinksinthenet.Thisisespeciallyusefulwhenyouarecreatingsomethingforanend-userwhodoesnotcarehownodesarelinkedtogether(thenyoumayalsowanttohidesomenodes).Toavoidconfusion,itisnotpossibletodisplaysomelinksandhideothers(althoughifthenodesatbothendsofalinkarehidden,thelinkbetweenwon'tbedrawneither).

Technical:Theremaining3choicesoftheStyle→LinksmenuareforthosefamiliarwiththeprocessofBayesnet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compiling,andwishtoseehowitisbeingdone.Theyallowyoutoswitchbetweenshowingthelinkstructureofthenetwhichwasoriginallyconstructed(Style→Links→RegularDag),thelinkstructureofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Markov_network.htm');returnfalse;">Markovnetderivedfromit(→MarkovNet),andthelinkstructureofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_triangulated.htm');returnfalse;">triangulated

netderivedfromtheMarkovnetwork(→Triangulated).

Thetriangulatednetisusedinternallytodeterminethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clique.htm');returnfalse;">cliqueswhencompilingthenet,andanumberisdisplayedwitheachnodetoindicateitspositioninthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_elimination_order.htm');returnfalse;">eliminationorderofthecompilation.

TheTriangulatedandMarkovNetstylesareonlyforviewingthenet,printingit,andcopyingitsgraphics(withnonodesselected).IfyoutrytodoanyotheroperationthestylewillautomaticallychangebacktoRegularDag.Beforeyouchoosethesefromthemenu,youmaywanttosaveyournet,sincetheywilllooseinformationaboutlinkbends.

CopyingandPastingGraphicsAftercopyingorcuttingallorpartofanet,youcanpastethegraphicsintootherWindowsapplications,suchasMicrosoftWord,PowerPoint,Works,etc.Ifsomenodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectedwhentheCopycommandisdone,thengraphicsforonlythosenodeswillbeplacedinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboard.Ifnonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,thengraphicsforthewholenetwillbe.Thenodeswillbedrawnwiththesamedesignstyleastheyareshownonthescreen,soyoumaywanttoadjustthestyleoptionsbeforecopyingtotheclipboard.

Shape:Afteryoupastethegraphicintoanotherprogram,youmaywanttoadjustitssizeandshapesothattheaspectratio(i.e.height/widthratio)issimilartotheBayesnetitcamefrom,inordertoachievethebestappearance.Iftheaspectratioisverydifferentfromtheoriginal,someofthecharactersmayoverlap.

IntoWord:Neticagraphicsarepastedintootherprogramsas“enhancedmetafiles”.WhenpastingintoMicrosoftWorditisoftenmoreconvenienttohavethegraphicasaMicrosoftWord“picture”.YoucanachievethisbyfirstpastingitintoWord,thenwhileitisstillselecteddoaCut,thendoanEdit→PasteSpecialandchoose“Picture”fromthedialogbox(andperhapsremovethecheckfrom‘floatovertext’).SometimesWorddoesnotdoaperfectjobofconvertingit,butjustdouble-clickingonthegraphictobringupthepictureeditor,andthenclosingitagainwithoutmakinganychanges,seemstofixanyimperfections.

Bitmap:Ifyouwanttopasteanetintoabitmapprogram,suchas“Paint”(whichcomeswithMicrosoftWindows),itisrecommendedthatyoupressALT+PRINTSCREENwhileNeticaisthecurrentapplication.ThecontentsofthewholeNeticawindowwillbeplacedintheclipboardinbitmapform,soyou

canpasteitintowhateverprogramyouwant,andtheneditittoremovepartsoftheimageyoudon’twant.

PrintingYoucanprintanetonaprinterwithFile→Print,orfromthecommandline.FirstyoumaywanttouseFile→PrinterSetuptoselectprintingoptions,suchaspagesize,margins,magnification/reduction,andwhichprintertouse.AfterpressingOkayonthefirstdialogboxwhichcomesup,ifthediagramislargeenough,youwillbequeriedforhowmanypageslargeyouwanttheprintingtobe(defaultistoappearononepage).Ifyouleavethoseentriesblank,thenyouwillbequeriedforaprintermagnificationinstead(defaultis100%).

Multi-Page:Ifthenetdiagramislargerthanonepage,thentheprinterwillprintpartsofitonseparatepagesinsuchawaythatthepagescanbetrimmedandthenattachedtogethertoproducetheoveralldiagram.Ifyouwishtoseewhatpartofthediagramwillenduponwhichpage,youcanturnonthepagebreaksby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">togglingLayout→ShowPageBreaks.Thiswilldrawlightbluelinesatthepagedivisions,whichcanalsobeusefulforvisualizingyourdrawingsize.

Whenyouchangethemagnification/reduction(ormargins,etc.)usingFile→PrinterSetup,thepagebreaklineswillshiftshowinghowmuchfitsoneachpage.

IfyouwantreallyprofessionalgraphicsresultsfromNeticauseSVGs.

SVGGraphicsNeticacangenerateveryhighqualitygraphicsforprintpublishingorwebsiteconstruction.ThesegraphicsareinaformatknownasSVG,whichstandsfor"scalablevectorgraphic".ItisthemainXMLbasedformatforgraphics,andsinceitisavectorgraphic,theimageslookverygoodatallresolutions,andthefilesizesareverysmall.(Neticacanalsomakeothervectorgraphics).

SVGwasjointlydevelopedbyW3C,Adobe,Sun,Apple,IBM,etc.Microsofthasstatedthatalltheirrelevantproductswillsupportit(thelatestversionofMSVisionowdoes).SVGgraphicscanbeimportedintomostmodernAdobeproducts,foreditingorconvertingtoothergraphicsformats.TheFirefox(Mozilla)andOperabrowsersnativelysupportSVGgraphics,andvariousplug-insareavailablefortheMicrosoftbrowser.

HowTo:HaveNeticadisplayyourBayesnetinthedesiredstyle,makesureitisthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activewindow,andchooseFile→MakeSVGGraphic,orpressCTRL+G.Ifyouwantthegraphictobeofasubsetofthenet,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthedesirednodesfirst.ThedefaultformatthatNeticawillgenerateisSVGZ,whichisacompressedSVG.SVGZisgenerallyabetterchoicebecauseithasasignificantlysmallerfilesize,producesexactlythesameimage,andmostprogramscanworkwithit.IfyouneedaregularSVG,eitherbecauseitisforsomeprogramthatcan'tworkwithSVGZ,orbecauseyouwanttoexamineoredititwithatexteditor(orXMLeditor),thenchoose"GraphicsFile-XML(.svg)"fromthedrop-downmenuatthebottomoftheSaveAsdialogboxthatappearsduringgeneration.

ImageEditing:OnceanSVGhasbeenmade,youcanopenitwithMicrosoftVisioandedittheimage.Nodeswillactaswholeobjects,sotheycanbemoved,resized,scaled,etc.Ifyouwanttoeditsomefeaturewithinanode,youmustfirst"ungroup"thenode,withShape→Grouping→Ungroup.Youcanalsoaddtitlesandgraphics,changecolorsandtheliketomakesharp

presentationpieces.

MicrosoftBrowser:SinceMSInternetExplorerdoesnotyetnativelysupportSVG,itrequiresaplug-in.Thereareseveralavailable,butcurrentlythebestistheonefromAdobe,sinceitcandozoomingandpanning.Thatplug-inusuallygetsquicklyandpainlesslyinstalledovertheinternetassoonasExplorertriestodisplayanSVG(afterputtingupadialogboxaskingifyouwantitinstalled).Ifyoudon'tseethedialogbox,thenyoucangettheplug-infrom:

http://www.adobe.com/svg/viewer/install/main.html

Examples:IfyouwishtoseeexamplesofSVGsgeneratedfromBayesnetsandhowtobuildawebsiteusingthem,see:

http://www.norsys.com/netlibrary/index.htm

WebsiteConstruction:ToaddanSVGgraphictoawebpage,youcanputthe.svgor.svgzfileinthesamedirectoryastheHTMLfileforthewebpage,andintheHTMLfileput:

<embedsrc="myFile.svgz"width="100%"height="100%"pluginspage="http://www.adobe.com/svg/viewer/install/">

Thewidthandheightattributesarenotstrictlynecessary,butareoftenuseful.

NotethatAdobenolongerrecommendsusingtheOBJECTtag(seehttp://www.adobe.com/svg/viewer/install/mainframed.html

Forthewebserver,youprobablydon'thavetodoanything,sincerecentversionsofwebservers(Apache,IIS,etc.)arealreadyproperlyconfigured,butforolderversionsyouneedtoaddtotheirmime-typetablethattheofficialMIME-typeforSVGandSVGZdocumentsis:

image/svg+xml

TheaboveinformationwasvalidasofOct2006,butsincebrowsersoftenchange,itmaybewisetoGoogleforthelatestrecommendationsfromAdobe,Microsoft,Mozilla,Opera,etc.Usefulsitesinclude:

http://www.adobe.com/svg/indepth/pdfs/ReadMewin.pdf

http://www.adobe.com/svg/viewer/install/mainframed.html

http://svg-whiz.com/wiki/index.php?

title=Server_Configuration

http://svg-whiz.com/wiki/index.php?title=MIME_Type

http://www.mozilla.org/projects/svg/faq.html

ForsupportingolderversionsofFirefoxandOperathatdonotsupporttheEMBEDtag,wehavefoundthefollowingtowork:

<head><scriptlanguage="Javascript">vari.e.=false;</script><!--[ifIE]><scripttype="text/javascript">i.e.=true;</script><![endif]--></head><body><scriptLANGUAGE="Javascript">if(i.e.){document.write('<embedsrc="myFile.svgz"width="100%"height="100%"

pluginspage="http://www.adobe.com/svg/viewer/install/">');}else{document.write('<objectdata="dir/myFile.svgz"width="100%"

height="100%"type="image/svg+xml"></object>');}</script></body

ReportsandDataLinkingThepurposeofNeticareportsisto:displayinformationin=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_file.htm');returnfalse;">textformonthescreen,sendittoaprinterorafile,orpasteitintoawordprocessingorspreadsheetprogram.SomeinformationcanalsobesentbyhotlinkstoMicrosoftExcel,orNeticacanbelinkedtoaprogramyoucreateusingNeticaAPI.

FromtheReportmenu,youcangeneratereportson=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTtablesofnoderelations,thefindingscurrentlyentered(i.e.thecase),beliefsforthecurrentcase(i.e.posteriorprobabilities),summarystatisticsonthewholenet,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontreestructureandtheeliminationorderusedforcompiling,oralistofthecurrentlyselectednodes.Neticacanalsogeneratereportsonutility-freesensitivityandhowwellaBayesnetperformswithrespecttoadataset.

HowTo:TheReportmenuconsistsofthreegroupsofitems,separatedbyhorizontalmenulines.Tomakeareportyounormallychooseitemsfromthesecondgrouptodeterminewherethereportwillbesent,anditemsfromthethirdgrouptochoosethereportoptions.Thenmakeachoicefromthefirstgrouptogeneratethereportonthedesiredsubject.

Seealso:UserReports

ReportSubjectsNeticacangeneratetextreportson:

Network Summaryinformationonthewholenet.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_whole.htm');returnfalse;">EXAMPLE

CustomReport Tailoredinformationonanode(s)orthewholenet.

Findings(Case) The=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings(i.e."case"or"evidence")currentlyentered,includinglikelihood("virtual")findings.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_findings.htm');returnfalse;">EXAMPLE

Equations Alistofall=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equationsofnodes.ChoosingtheHorizontalFormatoptionprintsthemininternalform.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_equations.htm');returnfalse;">EXAMPLE

Beliefs Thecurrentbeliefs(i.e.posteriorprobabilities)fornaturenodes,andexpectedutilitiesfordecisionnodes.typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_beliefs.htm');returnfalse;">EXAMPLE

Node-Sets Thelistofnodeswithintherequestedset.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_nodesets.htm');returnfalse;">EXAMPLE

CPTTables Thenoderelationasaconditionalprobabilitytable(

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontable.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_CPT.htm');returnfalse;">EXAMPLE

ListofSelected Alistofthenamesofthenodescurrentlyselected.typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_listselected.htm');returnfalse;">EXAMPLE

=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">JunctionTree

Detailsofthenetcompilationprocess.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_junctiontree.htm');returnfalse;">EXAMPLE

EliminationOrder Theorderusedduringcompiling.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_elimination.htm');returnfalse;">EXAMPLE

LinkstoExcel Hot-linkstothenodebeliefs.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_excel.htm');returnfalse;">EXAMPLE

EachoftheaboveisanitemoftheReportmenu,andchoosingitwillgeneratethatreport.Youcanalsosetoptionsorchangethedestinationofthereport.

WhichNodes:TheNetwork,JunctionTreeandEliminationOrderreportsalwaysapplytothewholenet.ListofSelected,CPTTablesandLinkstoPasteinExcelreportsapplyonlytothenodescurrentlyselected.Theothersapplytotheselectednodesifsomeareselected,orthewholenetifnoneare.

IftheFindingsreportisdonewithnodesselected,theywillallbelistedinthereport,buttheirfindingswillbeleftblankiftheydon’thaveone.Ifnonodesareselected,onlythosenodeshavingafindingwillbelisted.

Dimmed:JunctionTreeandEliminationOrderwillbedimmedifthenetisnotcompiledListofSelected,CPTTablesandLinkstoPasteinExcelwillbedimmedifnonodesareselected.

ListofSelectedcanbeusedtosavethecurrentsetofselectednodes,tolaterberestoredwithEdit→SelectNodes→ListedinClipboard.ItisalsousefulafteranEdit→FindAllsearchtogenerateatextlistofthefoundnodes.

ReportDestinationsReportscanbesenttoanyof:

•To=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">MessagesWindow•Copyto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">Clipboard•ToFile

EachoftheaboveisanitemoftheReportmenu,andchoosingtheitemwill=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggleitonoroff.Ifthereisacheck-markbesidetheitem,thenwhenareportisgenerateditwillbesenttothatdestination(soitmaygotomultipledestinations).

IfCopytoClipboardischeck-marked,thenaftergeneratingthereportyoucansimplypasteintoatexteditor,spreadsheetprogram,wordprocessor,etc.Ofcourse,youcanalwayshavethereportsenttotheMessagesWindow,whereyoucanlookatitoreditit,thencopyitfromthereandpasteit.However,ifitistoolarge,itmaynotfitintheMessagesWindow.

IfyouchooseToFile,youwillbeaskedwhichfiletosenditto.Ifyouwishtoremovethecheck-markfromToFile(sooutputisnotsentthere),chooseReport→ToFileandwhenthedialogboxappears,clickitsCancelbutton.YoucanusethereportoptionReport→AppendtoFiletodeterminewhethertooverwriteanexistingfile,orappendtoit.

IfitisannoyingyouthattheMessageswindowkeepscomingtotheforegroundwhensendingareporttotheclipboardorafile,thenuncheckToMessagesWindow.

ReportOptionsThereportoptionsare:

•IncludeNames•HorizontalFormat•TabSeparators•AppendtoFile

EachoftheseisanitemoftheReportmenu,andcanbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggledonandoff.

IfIncludeNamesischeck-marked,thenthenamesofnodesandstateswillbeincludedinthereportsforfindings,relationCPT,beliefsandbelieflinks,otherwiseonlythenumberswillappear.Whethernodesarereferredtobyname,titleorboth,canbesetbychangingthestyleofthenet.

HorizontalFormateffectsonlytheequations,findings,beliefsandbelieflinksreports.Ingeneralitproducesamorecompactreport,especiallyifnodeshavethesamestatenames.Forequations,itshowstheinternalrepresentationoftheequation.

TabSeparatorsshouldbecheck-markedifyouaregoingtopastethereportintoaspreadsheet(suchasExcel).Ifyouarepastingintoawordprocessingprogram(suchasMSWord),theneitherusespaceseparatorsandchangethefonttoamono-spaceoneafterpasting(suchasCourier),orusetabseparatorsandadjustthetabpositionsofthepastedtexttoproducepleasingcolumns.

LinkingwithExcelUsingreports,NeticacansendthebeliefsitcalculatestoanExcelspreadsheet.DescribedelsewhereisNetica'sabilitytolearnfromcasesusingExcel.

HowTo:FromtheReportmenu,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">toggletheoptionsHorizontalFormatandIncludeNames,dependingonhowyouwantthereporttolookinExcel(theotheroptionsareignored).=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">Selectthenodesofinterest,andthenchooseReport→LinkstoPasteinExcel.Thebelieflinks(AKAhot-links)willbeplacedinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clipboard.htm');returnfalse;">clipboard(thedestinationchoiceisignored).

Then,clickinasinglecellofanyExcelsheet,andpaste.Onceyouhavepasted,thebeliefnumberswillappearinExcel,andwillautomaticallychangewhenevertheychangeinNetica(forexample,asaresponsetoenteringafinding).

Beautifying:Whilethepastedcellsarestillselected,youmaywanttochooseFormat→Cells…fromExcel,clickontheAlignmenttabofthedialogboxwhichappears,andthenchooseHorizontalLeft.Itmaylookbettertowidensomeofthecolumns.Youcandeleteanyofthepastednamesornumbersyouarenotinterestedin,andcutandpastetheotherstomovethemaround.Theycanbeusedastheinputforanyequation,etc.,justlikeanyothercellinExcel.

NeticaExits:IfyoustoptheNeticaprogram,whileExcelwiththelinksisstillrunning,thebeliefnumbersusedwillsimplybethelastonesNeticaproduced.IfyourestartNeticathenExcelwillcontinuetousetheoldnumbersuntilyoutellittoreconnecttoNeticabyclickingonanycellwithalinkinit,thenclickinginthe"fx"textboxforeditingthecellscontents,andthenclickingthegreencheck-mark,orpressingtheENTERkey.

Alternately,youcanchooseEdit→Links…fromthemenu,andinthedialogboxthatcomesup,clickonthefirstlinkandthenSHIFT-clickonthelastonesotheyareallselected,andthenclicktheUpdateValuesbutton,andthentheClosebutton.Afterthedialogboxisgone,thelinkswillbereconnectedandwillremainso.

ExcelExits:IfyoustopExcelwhileNeticaisstillrunning,andthenrestartExcelandopenthespreadsheetwithlinks,thereconnectionwillbemadeautomatically.IfsomenetshavetobereadintoNeticabecauseExcelreferstothem,and/orcompiledorupdated,thatwillhappenautomatically.

Troubleshooting:TotroubleshootExcellinkswithNetica,ortocontroltheirbehavior,checkthefollowing:Edit→Links…Theyshouldhave"A"inthe"Update"columntoupdateautomatically.Tools→Options→Calculation→UpdateremotereferencesshouldbecheckedTools→Options→General→IgnoreotherapplicationsshouldNOTbecheckedTools→Options→Edit→AsktoupdateautomaticlinksEdit→PasteSpecialisnotrequiredwhenpastingthelinks.

LinkingwithNeticaAPI=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_Application.htm');returnfalse;">NeticaApplicationcanbeusedtoprovideauserinterfacefor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPI.Bayesnetscanbedisplayedintheusualway,findingscanbeenteredandbeliefsdisplayed,withNeticaAPIautomatingNeticaApplication.

ThisisanexcitingnewfeaturethatisbeingexpandedwitheachnewreleaseofNetica.InmanycasesitallowsyoutowriteashortprogramthatextendsthefunctionalityofNeticaApplication,orashortprogramthatcompletelycontrolsNeticaApplicationtodosomespecificfunction.

NeticaAPI(embeddedinyoursoftware),runsconcurrentlywithNeticaApplication,asaseparateprocess,andtheycommunicatewitheachother.Thecommunicationiscompletelytransparenttoyou;allyoudoiscalltheregularNeticaAPIfunctions,andallthedetailsaretakencareof.

ThesecapabilitiesarebuiltintoversionsofNeticaafter3.17.Contact=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsystoobtaindocumentationonusingthem.AversionofNeticawithaCOMinterface(ActiveX)hasnowbeenreleased,whichprovidesyetanotherconnectivityoption.

GeneratingUserReportsYoucanuseNeticatodisplayinformationorreportwindows,calleduserreports.Thepurposeismainlytoprovideextrainformation,assistanceordirectionseithertodevelopersortootherswhomaybeusing/viewingyourBN.Auserreportcouldbeassimpleasatextmessagegivingamoredetaileddescriptionofanode.Oritcouldbemorecomplex,suchasthecurrentbeliefprobabilitiesofanode-set,orasensitivityanalysisofquestionswithrespecttothetargetnode.

UserreportsareoftenusedwithNetica-Web,astheycanalsobecreatedfortheuseronthecurrentcaseorinferredresults,whichcanbeprintedoutorsavedtofile.TheycanalsobeusedfromtheAPI.

TheNeticamechanismtosupportthisiscalledcustomreports.Youcancreateatemplatefileormodifyanexistingtemplate(usuallyinHTMLwithspecialnotationsforreportelementstobeinserted)whichdefineswhatyouwanttohavedisplayed.YouthenaccessthattemplatefilefromyourBayesnet.Atemplatefilecanbeusedtogenerateareportontheoverallmodel(i.e.Bayesnet),oritcanapplytoindividualquestions(i.e.nodes).Inthefirstcase,itiscalledanettemplatefile,andthetagswithinitstartwith"Net",andinthesecondcaseitiscalledanodetemplatefile,withtagsthatstartwith"Node".

Seealso:ReportsandDataLinking

AddingaReportAddingandcreatingcustomreportstoyourtemplatefolderisquickandsimple:

1.Createorcustomizeareporttemplatefile.

2.Editandsavethetemplate.

3.Selectthedesirednode(s)andchooseReport→CustomReport.

1.Createareportfile:Thefirststepistocreatetheuserreportfile.Theeasiestwayistouseanexistingreporttemplatefile,ormodifyonethatissimilartowhatyouwant.Tofindexistingtemplatefiles,lookintheReportTemplatesfolder,whichisinthesamefolderastheNeticaexecutable:Netica.exe(thepathtothisfolderisprintedoutintheMessageswindowofNeticaApplicationwhenitfirststartsup).

2.Editthetemplate:Youcanopenandeditan.htmfiledirectlyinNetica,bychoosingFile→OpenasText.However,thedefaulttemplatesareHTMLfiles,soyouwillprobablywanttouseatexteditorthathasspecialfacilitiesforHTML(suchasVisualStudio.YouconstructthetemplatefileoutofnormalHTMLcode,butyouputspecialtagswhereyouwantNeticatoinsertinformation.

Thetagsconsistofdoubleopeningsquarebrackets[[followedbyoneofthetagnames,possiblyfollowedbysomeextradirectionsinparenthesis,andendingwithtwoclosingsquarebrackets]].Youcanrefertonodesaccordingtotheirnumberoraccordingtotheirname.Forselection,thenodethatyouselectfirstwillbeconsideredNode(0).ThesecondnodeselectedwillbeSelNode(1).

Fornumber,write:[[Node(0).someInstruction]]

Forname,write:[[Node("nodename").someInstruction]]

Thensaveyourtemplatefilewhereveryouwish.Ifyouaremakinghtmfiles,theextensionshouldbe'.nsp.htm'.ItisprobablybestnottosaveyourtemplatesinthesamefolderastheonesthatcomewithNeticaApplication,justsotheydon'tgetmixedup.

3.Generatetheuserreport:Next,selectthedesirednode(s)andchoose

Report→CustomReporttogeneratethetailored"report".Fromthefiledialogwhichappears,pickthetemplatefileyouhavejustcreated.Inamomentyourbrowsershoulddisplaytheresultsofyourreport.Note:thereportwillbedisplayedinwhateverformatitwascreated(e.g.htmfileswillbedisplayedinaninternetbrowserwindow,docfileswillbedisplayedinMicrosoftOfficeWord,etc).

ReportsonMultipleNodes:Youcanrunacustomreportonasinglenode,multiplenodes,ortheentirenet.Torunareportonmultiplenodes,firstselectthenodesthenchooseCustomReport.Openthetemplatefileyoucreatedforthosenodes,whichshouldcontaintextwiththeprefix:[[SelNode(0).someInstruction]].Remember,thenodeyouselectfirstwillbeconsideredNode(0).

AvailableUserReportTagsThefollowingtagsmayappearinanyreporttemplatefile,indoublesquarebrackets.Theywillbereplacedwithareportaccordingtotheirdescription.Foranexampleoftheiruse,seethefile"ReportTemplates\NetAll.nsp.htm".Foreditingtips,seeitem2ofaddingareport.

Net.BeliefsTableReportonallthebeliefsinthenet.Canbedisplayedintextorhtmlrespectively,asNet.BeliefsTable(TextFormat)andNet.BeliefsTable.

Net.CaseIDTheIDnumberofthecasecurrentlyreadintothefindings.Net.CaseProbabilityThejointprobabilityofthefindingscurrentlyentered,aspredictedbythenet.

Net.CaseExpectedUtilityTheexpectedutilityofthefindingscurrentlyentered.

Net.CommentCommentsmadewithinthenetorthenetdescriptionNet.EliminationOrderList(Seperator=",")Theeliminationorderusedtoconstructthejunctiontree.

Net.Equations(Compiled)Reportonalltheequationswithinthenet.Ifthe"Compiled"tagisleftout,thentheequationswillappearintextasentered.WiththeCompiledtag,theequationappearsinaninternal(text)format,whichissometimesilluminating.

Net.FileNameFilenameshouldendin.netaNet.FindingsList(Equals="=",Seperator=",")

Reportonallthefindingswithinthenetinlistformat.Net.FindingsTableReportonallthefindingswithinthenetintableformat.Canbedisplayedintextorhtmlrespectively,asNet.FindingsTable(TextFormat)andNet.FindingsTable.Ifyouwantthequestionslistedvertically,youcanuse:Net.FindingsTable(VerticalFormat)

Net.GraphicReportonnetgraphics.Notavailableonmostsystems.Net.JunctionTreeTable(TextFormat)Reportonthenet'sjunctiontree.

Net.ModifyDateDateBayesnetfilewaslastmodified.

Net.NameNameofthenet.Net.NodesetTableReportonthenode-setswithinthenet.Canbedisplayedintextorhtml,asNet.NodesetTable(TextFormat)orNet.NodesetTablerespectively.

Net.OverallTableReportontheoverallnet.Canbedisplayedintextorhtml,asNet.OverallTable(TextFormat)orNet.OverallTable(StyleHtml=tableOverall).Thisreportcontainsgeneralnumericmeasurementsonthenumberofnodesofeachtype,numberoflinks,numberoffindings,numberofloops,andnumberofCPTsetc.

Net.TitleTitleofthenet.Net.User(Field="..")Thevalueofthenameduserfield.EspeciallyusefulwhenbuildingNetica-Webprojects.

NodeTagsThefollowingtagsmayappear,indoublesquarebrackets,inareporttemplatefilemeantforanode.Theywillbereplacedwithareportaccordingtotheirdescription.Foranexampleoftheiruse,seethefile"ReportTemplates/NodeAll.nsp.htm".

Node.BeliefsList(Seperator="</td><td>")

Node.Comment

Node.CPTable

Node.CPTable(Experience)

Node.CPTable(TextFormat)

Node.Equation(Compiled)Thisnodesequation,ifithasone.Ifthe"Compiled"tagisleftout,thentheequationwillappearintextasentered.WiththeCompiledtag,theequationappearsinaninternal(text)format,whichissometimesilluminating.

Node.Finding

Node.HoverComment

Node.InputName(Parent=0)

Node.IsDeterministic

Node.Kind

Node.Label

Node.MutualInfo(Node="TargetNode(0)")

Node.MutualInfo

(Node="TargetNode(0)",Fraction=Percent)

Node.MutualInfo(Node=0)

Node.MutualInfo(Node=0,Fraction=Percent)

Node.Name

Node.NumberStates

Node.Real(State=0)

Node.RelativesList(Generation=-3,Seperator=",")

Node.RelativesTable(StartGeneration=-4,

EndGeneration=2,StyleHtml=table)

Node.SensitivityTable(MutualInfo)

Node.SensitivityTable(TextFormat,MutualInfo)

Node.StateComment(State=0)

Node.StateLabelsList(Seperator="</td><td>")

Node.StateName(State=0)

Node.StateTitle(State=0)

Node.ThresholdLower(State=0)

Node.ThresholdUpper(State=0)

Node.TitleNode.Type

Node.VarianceReal

(Node=0,IndicatesUnknown="unknown")

Node.VisualPositionNode.VisualStyle

Built-InGenericReportTemplateFilesNeticacomeswithanumberofpre-madetemplatefilesforcommontypesofreports,andtheymightbejustwhatyouneed.Ifyourequireamorecustomizedapproach,youcancreateyourowntemplatefile.Ifso,youmaywanttouseoneofthegenericonesasastartingpoint,orexamineitforideasonhowtomakeyourown.

Location:YourNeticadownloadcomeswithabatchofpre-madereporttemplates.InthemaindirectoryofyourNeticainstallation,youwillseeafoldercalledReportTemplates(thepathtothisfolderisprintedoutintheMessageswindowofNeticaApplicationwhenitfirststartsup).

ThegenericfilesNetAll.nsp.htmandNodeAll.nsp.htmareespeciallyuseful,sincetheycontainmanypossiblemethodsfordisplayinginformation.

Forexample,forareportonthetableofanode,youcoulduse:Generic/ReportTemplates/NodeTable.nsp.htm

Hereisalistofthegenericreportsavailable:

NetAll.nsp.htmNetBeliefs.nsp.htmNetCase.nsp.htmNetComment.nsp.htmNetCommentUnformatted.nsp.htmNetDeveloper.nsp.htmNetEquations.nsp.htmNetFindings.nsp.htmNetGraphic.nsp.htmNetSensitivity.nsp.htmNetUser.nsp.htmNodeAll.nsp.htmNodeDescription.nsp.htmNodeDeveloper.nsp.htm

NodeEquation.nsp.htmNodeParents.nsp.htmNodeSensitivity.nsp.htmNodeTable.nsp.htmNodeUser.nsp.htmNodeWeb_Description.nsp.htm

EquationsTherelationshipbetweenanodeanditsparentnodescanbeenteredusinganequationifdesired.Thisispossiblewhetherthenodesarecontinuousordiscrete,andwhethertherelationshipisprobabilisticordeterministic.Neticawillconvertallequationsintotables(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontable)beforecompilinganet,doingnettransforms,orexpandingaDBN.Thetablesarethenusedinthesamewayasifyouhadenteredthembyhand.

ThefollowingsectionsoutlinefurtherinformationonNetica’sequations:

•UsingEquations•Syntax•ConvertingtoaTable•ComparisontoJava/C/C++•Conditionals•Link(Input)Names•StateNamesasConstants•DiscreteVariableswithStateValues•InternalFormofEquations•ConstantNodesasAdjustableParameters•ExamplesofEquationUse•Built-inConstants•Built-inFunctionsandDistributions

UsingEquationsFollowthesestepstoenteranduseanequationtorepresentanode’srelationshipwithitsparents:

1.Entertheequationintothenodedialogboxinthecorrectform,perhapsusingbuilt-infunctions.Herearesomeexamples.

2.Ifthenodeiscontinuous,orhasanycontinuousparents,theymustbediscretized.

3.Converttheequationtoatable.

4.Usethenet(e.g.compileit,dobeliefupdating,absorbnodes,reverselinks,orsolvedecisionproblems).Neticawillusethetablegeneratedfromtheequation.

Ifyouchangetheequationforanode,orthediscretizationofthenodeoranyofitsparents,orthevalueofarelevantconstantnode,youmustrepeatstep3abovebeforethechangestakeeffect.

Tips:

•Iftheequationsgetlarge,itmaybeeasiertocreatethemina=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditor,andthenpastethemintothenodedialogbox.•Wheneditinganequationyoucancut,copy,paste,undo,etc.usingtheirCTRLkeycommands,orby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clicking.•Ifthereisamistakeinthesyntaxoftheequation,Neticawillpopupanalertboxwithanerrormessage.Ifnecessary,movethealertboxsothattheequationisunobscured,andthenclickonthetitlebaroftheNodePropertiesDialogbox.ThatwillcausetheNodePropertiestobecometheactivewindow,andaselectionpointwillappearintheequationtextclosetowheretheerrorislocated.•Youcanprintoutalltheequationsinthenet,orselectthenodeswith

equations.•Ifyouneedtodefineintermediatevariablestosimplifytheequations,implementthemasnew(intermediate)nodes.•Thetablesgeneratedbyequationsmayresultinlargefiles(andthereforeslowreading),soyoumaywantremovethenode’stablewithTable→Removeor beforesavingthenettofile.Whenyoulaterreaditin,doTable→EquationtoTableor (withnonodes=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected)beforeusingit.

EquationSyntaxNeticaequationsfollowmostoftheusualstandardsformathematicalequations,andaresimilartoprogramminginJava,CorC++.Theusualmathematicaloperators(+,-,*,/,etc.),andtheusualfunctions(min,abs,sin,etc.)canbeused,parenthesisareusedforgrouping,andnumericconstantsareintheirusualform(e.g.3,-4.2,5.3e-12).

Left-HandSide:Thepartofanequationtotheleft-handsideoftheequalssymbolforadeterministicnodeconsistsofthenameofthenode,anopenparenthesis,alistofthenamesofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsseparatedbycommas,andacloseparenthesis(ifyouhavedefinedlinknames,youmustusethoseinsteadofparentnames).Forinstance,iftheequationisfornodeX,andtheparentsofXareVel,dtandsigma,theleft-handsidecouldbe:

X(Vel,dt,sigma)=...

Notethatspacesarenotrequired,andtheremaybemorespacesifdesired.

Forprobabilisticnodes(i.e."=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_chance_node.htm');returnfalse;">chancenodes"),theleft-handsideconsistsofalowercase"p",anopenparenthesis,thenameofthenode,averticalbar,alistofthenamesoftheparents(orlinknames)separatedbycommas,andacloseparenthesis.Ifthenodementionedabovehadbeenaprobabilisticnode,thelefthandsideofitsequationcouldbe:

P(X|Vel,dt,sigma)=...

Right-HandSide:Theright-handsideofanequationmayconsistofnumbers,adjustableparameters,statenames,conditionals,referencestothevariables(i.e.parentnodes),andbuilt-inconstants,functionsoroperators.

NodesAllowed:Theonlynodeswhichmaybementionedinanequationare:thenodetheequationdescribes,itsparents,andanyconstantnode.

Errors:Ifthereisamistakeinthesyntaxoftheequation,Neticawillpopup

analertboxwithanerrormessage.Ifnecessary,movethealertboxsothattheequationisunobscured,andthenclickonthetitlebaroftheNodePropertiesDialogbox.ThatwillcausetheNodePropertiestobecometheactivewindow,andaflashingcursorwillappearintheequationtextclosetowheretheerrorislocated.

Comments:Commentscanbeembeddedinequations,andtheywillbeignoredbyNetica.Everythingbetween/*and*/willbeinterpretedasacomment,aswilleverythingbetween//andtheendoftheline.Asmanyspacesorlinebreaksasdesiredmaybeplacedbetweenanytwosymbols.

AllValues:Iftheequationisforaprobabilisticnode,itsright-handsidemustprovideaprobabilityforallthenode’spossiblevalues(sothenameofthenodemustappearthereatleastonce).Forexample,ifnodeColor(withstatesred,orange,yellow)hasparentTemp(withstateslow,med,high),itsequationcouldbe:

p(Color|Temp)=

Temp==high?(Color==yellow?1.0:0.0):

Temp==med?(Color==orange?1.0:0.0):

Temp==low?(Color==orange?0.2:

Color==red?0.8:0.0):0

Ifyouusethebuilt-indistributions(suchasNormalDist),theaboveisautomaticallytakencareof.Oneexceptiontotheaboveisifanodeis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">boolean.Thenonlytheprobabilityforthetruestateneedbegiven.Forexample,ifnodeIt_Fallsisboolean,itsequationcouldbe:

p(It_Falls|Weight,Size)=

Weight/Size>10?0.10:

Weight/Size>5?0.03:

0.01

Examples:Herearesomeexamplesofequations:X(Vel,dt,X0)=X0+Vel*dt

p(X|Vel,dt,spread)=NormalDist(X,Vel*dt,spread)

Color(Taste)=

Taste==sour?blue:Taste==sweet?red:

Taste==salty?green:gray

p(Color|Taste)=

(Color==red&&Taste==sweet)?0.7:0.1

MoreExamples

ConvertinganEquationtoaTableBeforedoingmostnetoperations(e.g.compiling,absorbingnodes,reversinglinks,oroptimizingdecisions),eachinvolvednodemusthavearelationcontingencytable(e.g.its=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPT)toexpressitsrelationshipwithitsparents.Ifyouhaveenteredtherelationshipasanequation,thenatablemustbebuiltfromtheequation.

Tobuildtablesforparticularnodes,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodes,andthenchooseTable→EquationtoTableorclickthe toolbarbutton.Ifsomeoftheselectednodesdon’thaveequations,theywilljustbeskipped.Ifnonodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deselect_nodes.htm');returnfalse;">selected,thenNeticawillbuildtablesforallthenodeswhichhaveequations.

Ifanodewithanequation,oranyofits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parents,areforcontinuousvariables,thentheymustbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizedbeforeconvertingtheequationtoatable(excepta=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynode).WhenNeticadoestheconversion,itmustdecidewherewithineachdiscretized“cell”toevaluatetheequation.Itchoosesanumberofpoints(attrulyrandompositions)withinthecell,andusestheaverageoftheresultsobtained.Justbeforetheconversionprocess,Neticawillputupadialogboxaskingyouhowmanyrandomsamplestomakepercell.Thelargerthis

number,themoreaccuratetheresultswillbe,butthelongeritwilltake.

SamplingUncertainty:Sincethissamplingprocesscan’tcheckeverypointwithinthecell,itmaymissanarrowspikeorridge.Neticacanrepresentwithinthecreatedtabletheadditionaluncertaintyduetothesampling,oritcanassumethatthesamplingwastrulyrepresentative.Neticawillputupadialogboxaskingyouwhichitshoulddo.Itisbesttoignorethesamplinguncertaintywhenyouknowtheequationdoesn’thaveanynarrowspikesorridges.

Whenthesamplinguncertaintyisincluded,thennoneofthetableentrieswillbezero,sinceNeticacanneverbesurethatithasn’tmissedsomenonzeropointswithinthecell.Thesamplinguncertaintywillbesmallerifyouincreasethenumberofsamplespercell.SamplinguncertaintycanberemovedafterthetableiscreatedbychoosingTable→Harden,andprovidingadegreeof1.

Large:Thesizeofthetablegeneratedistheproductofthenumberofstatesofthenodewiththenumbersofstatesofeachofitsparentnodes.Soifanodehasmanystates,ormanyparents,thenthetablesmaybeverylarge,andNeticamayreportthatitdoesn’thaveenoughmemoryfortheoperation.Oritmayjusttakealongtime.Youcanalleviatetheproblembyeliminatingunnecessaryparentsandusingcoarserdiscretizations(perhapshavemorethanonenodeforthesamevariable,withdifferentdiscretizationsdependingonwhichnodeitisaparentfor).

EquationSyntaxvs.JavaorC/C++LanguagesTheequationsyntaxispreciselythesameastheJava(andCandC++)programminglanguages,excepttheparttotheleftoftheassignmentoperator(=)isdifferent,andnosemicolonisrequiredattheendoftheequation.

TheC/C++/Javabitwiseoperators(suchas&,|,~,^)arenotavailableinNetica,butthelogicaloperators&&,||,!are.InadditionNeticahasalogical‘xor’function(thebitwisexoroperator^ofC/C++/JavaisusedforthepoweroperatorbyNetica).

AlloftheCStandardLibrarymathfunctions(sin,log,sqrt,floor,etc.)areavailableandusethesamenames.

EquationConditionalsSupposecontinuousnodeXhastheparentsYandB.IfyouwantedtogiveP(X|Y)adifferentequationinvolvingXandYfordifferentvaluesofB,youcouldwritesomethinglike.p(X|Y,B)=

(B<2)?NormalDist(X,3+Y,1):

(B<6)?NormalDist(X,2+Y,3):

UniformDist(X,0,10)

Theconditionsareevaluatedinorder,sothefirstcoversallcaseswhereB 2,thesecondcoverscases2 B 6,andthelastcoverstheremainingcases(i.e.B 6).So,ifBislessthan2,Xisdistributednormallywithmean3+Y,ifitisbetween2and6thenthemeanis2+Y,andifitisover6thenXisdistributeduniformly.

Iftherearemoreparents,thissortofconstructcanbenestedtoprovideatreestructureofpossiblecontingencies.

Hereareacouplemoreexamples.Theyshowawaytoconditionoverthestatesofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenode:

p(X|Y,B)=

(B==yellow)?NormalDist(X,2,sqrt(Y)):

(B==orange)?NormalDist(X,4,Y):

(B==red)?NormalDist(X,6,Y^2):0

p(X|B)=

member(B,CA,TX,FL)?NormalDist(X,3,1):

member(B,MA,WA)?NormalDist(X,5,1):

member(B,NY,UT,VA)?NormalDist(X,7,2):

UniformDist(X,0,10)

Noticethatthe“fallthrough”caseofthefirstexampleissimplya0.ThisindicatesthatthedesigneriscountingonBtobeoneofyellow,orangeorred.IfBeverhasanotherstate,thenwhenNeticaisconvertingtheequationtoa

tableitwillgiveawarningmessagethat“forn/Nconditions,nononzeroprobabilitywasdiscoveredbysampling”(providingnosamplinguncertaintyisbeingadded).

Inthelastexample,thefallthroughcasegivesauniformdistribution.IfextrastatesarelateraddedtoB,thentheywilljustfallthroughandusetheuniformdistribution.

LinkNamesWhenyoufirststartworkingwithequations,youwillprobablyusethenamesoftheparentnodesinyourequations.However,sometimesyouwillwantamorelocalrepresentation,sothatyoucandisconnectsomeoftheparentsandhookthenodeuptonewparentswithouthavingtochangeallthenodenameswithintheequation.

Orperhapsyoucopyandpastethenodetousewithnewparents.Oryouputthenodeinanetfragmentlibrarywithoutanyparents,sothatitwillbesuppliedwithnewparentswhenitisused.Oryouwanttocopyandpastetheequationfromonenodetoanother,withoutchangingallthenodenames.

Thesolutiontoalltheseproblemsistouselinknames,sometimescalledinputnames.Theyprovideanargumentnameforeachlinkenteringthenode(andthereforeaproxyforeachparentnode).Youcansetthemwiththenodedialogbox.Yourefertotheminyourequationinexactlythesamewayyouwouldthecorrespondingparentname.Whenaparentisdisconnected,thelinknamewillremain.

Iflinknamesaredefinedforanode,theymustbeusedinsteadoftheparentnames.

StateNamesasConstantsYoucanusethestatenamesofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretenodeasconstantsinanequation.Forexample,ifnodeColorhasstatesred,green,blueandyellow,andnodeTemperaturehasstatescoolandwarm,youcouldwrite:

Temperature(Color)=member(Color,red,yellow)?warm:cool

SpecifyingNode:Eachstatenameonlyhasmeaningrelativetothenodeit’sfor.Usuallywhenyouuseastatename,Neticacanidentifythatnodefromcontext.However,ifNeticadoesn’tknowwhichnodeastatenamerefersto(e.g.itgivesanunknownvalueerrormessage),youcanindicatewhichnodebyfollowingthestatenamewithadouble-dashandthenthenameofthenode.Continuingwiththeaboveexample,ifnodeSwitchhadthestates0,1and2,youcouldwrite:

Color(Switch)=select0(Switch,red--Color,yellow,blue)

The“--Color”wasnotrequiredon“yellow”and“blue”,becausethecontextwascarriedoverfrom“red--Color”,butitcouldbeputthereaswell.

StateNumbers:Insteadofstatenames,youcanjustusethestatenumber(numberingstartsat0),butitishighlyrecommendedtousethenames,becausetheyaremorereadableandlesserror-prone.Also,itisnotasseriousiflaterstatesareaddedorre-ordered.

DiscreteVariableswithStateValuesWhenanodeequationcontainsa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariablewhichhas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">statevaluesdefined,thenumericquantitieswhichthatvariablesuppliestotheequationcouldbethestateindexesofthevariable,orthevaluesassociatedwiththestateindexes.Usuallyafunctionoroperatorwillassumeitisthevaluesthataredesired,butinafewcasesitwillusethestateindexes,forinstanceiftheotherargumentstoitarestateindexes.

Forexample,considertheequalityoperator,andadiscretevariableColor,whichhasvaluesandstatenames(suchasblue)defined.WhenColorappearsintheequation,itcouldrefertoastateindexofColor,ortothevalueassociatedwiththatstateindex.

Usesstateindex:Color==blueColor==#1#Color1==#Color2Usesstatevalue:Color==3.2Color==1Color1==Color2

Theaboveisfortheevaluationofequationexpressions.WhenitcomestoassigningtheresultoftheequationtoitsLHS(left-handside)variable,ifthevariableisdiscretewithvaluesdefined,thesameissuearises.Hastheequationcalculatedastateindexforthevariable,oravalueassociatedwiththestate?ThepurposeoftheAsStatefunctionistoindicatethatstateindexesshouldbeused.

Continuingwiththeexampleabove:

Assignsbyvalue:Color()=3Color1(Color2)=Color2Assignsbyindex:Color()=#3Color1(Color2)=AsState(Color2)Color1(X,Y)=AsState(integer(X/Y))

YoumaywanttoverifythatNeticaisdoingasyouexpectbyhavingitcalculateafewvaluesandchecking(forexample,byusingTable→EquationtoTable).OryoucanexaminetheinternalrepresentationoftheequationbychoosingReport→HorizontalFormatfromthemenuandthenReport→Equation.CheckforplaceswhereNeticahasinsertedthefunction"_levels"(mapsstateindex→realvalue),"_find0"(mapsrealvalue→stateindexofadiscretevariable),or"_discretize"(mapsrealvalue→stateindexofacontinuousvariable).

InternalFormofEquationsNeticaconvertsequationstoaninternalformforfastevaluation.Sometimesthatmeansextrafunctionsareinvokedthatweren'tintheoriginalequation;thesefunctionsalwaysstartwithanunderscore.

Youmayreceiveanerrormessagethatindicatestherewasaproblemevaluatingoneofthesefunctions.Generallythatoccursbecauseinyourequationyousupplyvaluestoafunctionthatareoutofitsdomain.

IfyouwanttoseewhattheinternalrepresentationoftheequationinNeticalookslike,youcangenerateareportbychoosingReport→HorizontalFormatfromthemenuandthenReport→Equation.

Someexampleinternalfunctionsare:

_not_discretize_find0

_levels_select0_Bernoulli

“Constant”NodesasAdjustableParametersYoucreateaconstantnodebyaddinganaturenodetothenet,bringingupitsnodedialogbox,andchoosing“Constant”fromthenodekindselector.Youcanalsosetothercharacteristicsofaconstantnodeinthesamewayasanyothernode,suchasgivingitstatenames.

Tosetorchangethevalueofaconstantnode,enterthevalueinthesamewayasyouwouldenterafinding.

ForEquations:Youcanrefertothevalueofaconstantnodeanywhereinanynodeequationbyusingitsnodenameasyouwouldaparentnode.Itshouldnotappearintheargumentlisttotheleftofthe=symbol.Nolinkisrequired.

Whenyouconverttheequationtoatable,thevalueofanyreferencedconstantnodeswillbeused.Ifyouchangethevalueofaconstantnode,youmustrebuildthetableforthechangetotakeeffect.

ExamplesofEquationUseHereareexampleequationsforsomecommonornon-obvioussituations:

StateComparisons:SupposethestatesofnodeSourceareCA,TX,FL,BCandNY.ThestatesofnodeDestareTX,NY,MAandUT.Wewanttoknowifcross-bordertravelisrequiredtotransportfromSourcetoDest,andthatisindicatedbythe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleannodeTravel.TheequationbelowworkseventhoughnodesSourceandDesthavedifferentsetsofstates,andinadifferentorder.

Travel(Source,Dest)=(Source!=Dest)

AdditiveNoise:Sayyouwanttorepresentsomethinglike:x1=x2+gauss(0,0.2)whichcouldindicatethatx1isthesameasx2,butwiththeadditionofGaussiannoisehavingmean0and =0.2.Youcoulddothisbydefininganewnodex3,andsettingtheequationsofx1andx3as:

x1(x2,x3)=x2+x3p(x3)=NormalDist(x3,0,0.2)

MultipleDiscretizations:Sometimesitisusefultousemorethanonenodetorepresentacontinuousvariable,anddiscretizeeachdifferently.Forexample,thecoarseronemaybeaparentforanothernodewhoseCPTwouldbetoobigwithafinerdiscretization,whilethefineronewouldserveasaparentfornodesrequiringmoreaccuracy.Putalinkfromthefinernodetothecoarser,andgivethecoarsernodeanequationlike:

X_d4(X_d12)=X_d12

Noisy-Or:Tocreateanoisy-ornode,justcreatearegular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleannaturenode,putlinkstoitfromthepossiblecauses,giveitanoisy-orequation,andusethattobuilditsCPT.Forextracomputationalefficiencyyou

maywanttoselectitandchooseModify→DecomposeEquationsbeforebuildingtheCPT.

Forexample,ifC1,C2andC3are=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleannodesrepresentingcausesofbooleannodeE,andtherearelinksfromeachCitoE,thenEcouldhavethenoisy-orequation:P(E|C1,C2,C3)=

NoisyOrDist(E,0,C1,0.5,C2,0.3,C3,0.1)

Foritsmeaning,seetheNoisyOrDistdescription.Thecauses,andeventhelinkparameters,canbemorecomplexexpressions(thenyouwon’tbeabletouseModify→DecomposeEquationsthough).

Forexample:P(Bond|Temperature,BackTemp,Pressure,Switch,Eff)=NoisyOrDist(Bond,0.001,Temperature>BackTemp,0.5,Pressure==high,0.3,Switch,0.9*Eff)

Built-inConstantsThefollowingconstantsmaybeusedinequations:

pi=3.141592654deg=radianperdegree=pi/180

Ifyouwishtohavetheconstante(=2.7182818)inyourequation,useexp(1).

Neticaalsocontainsanextensivelibraryofbuilt-infunctions.

Example: sin(35*deg)returnsthesineof35degrees

Built-inFunctionsNeticacontainsanextensivelibraryofbuilt-infunctionsandconstantswhichyoucanuseinyourequations.

Theprobabilitydistributionfunctionsallhaveanamethatendswith"Dist"(e.g.NormalDist).Theirfirstargumentisalwaysthenodeforwhichthedistributionisfor.SoifnodeXhasparentm,youcouldwrite:

P(X|m)=NormalDist(X,m,0.2)

toindicatethatXhasanormal(Gaussian)distributionwithmeangivenbyparentm,andastandarddeviationof0.2.

CommonOperatorsFunctionalNotation OperatorNotation

neg(x) -x

not(b) !b

equal(x,y) x==y

not_equal(x,y) x!=y

approx_eq(x,y) x~=y

less(x,y) x<y

greater(x,y) x>y

less_eq(x,y) x<=y

greater_eq(x,y) x>=y

plus(x1,x2,...xn) x1+x2+...+xn

minus(x,y) x-y

mult(x1,x2,...xn) x1*x2*...*xn

div(x,y) x/y

mod(x,base) x%base

power(x,y) x^y

and(b1,b2,...bn) b1&&b2&&...&&bn

or(b1,b2,...bn) b1||b2||...||bn

if(test,tval,fval) test?tval:fval

CommonMathabs(x) absolutevalue

sqrt(x) squareroot(positive)

exp(x) exponential(e^x)

log(x) logarithmbasee

log2(x) logarithmbase2

log10(x) logarithmbase10

sin(x) sine

cos(x) cosine

tan(x) tangent

asin(x) arcsine

acos(x) arccosine

atan(x) arctangent

atan2(y,x) atan(y/x)butconsidersquadrant

sinh(x) hyperbolicsine

cosh(x) hyperboliccosine

tanh(x) hyperbolictangent

floor(x) floor(highestinteger<=x)

ceil(x) ceiling(lowestinteger>=x)

integer(x) integerpartofnumber(samesign)

frac(x) fractionpartofnumber(samesign)

SpecialMathround(x)roundto(dx,x)approx_eq(x,y)eqnear(reldiff,x,y)clip(min,max,x)rect(x,a,b)sign(x)xor(b1,b2,...bn)increasing(x1,x2,...xn)

increasing_eq(x1,x2,...xn)avg(x1,x2,...xnmag(x1,x2,...xn)min(x1,x2,...xn)max(x1,x2,...xn)argmin0/1(x0,x1,...xn)argmax0/1(x0,x1,...xn)nearest0/1(val,c0,c1,...cn)select0/1(index,c0,c1,...cn)member(elem,s1,s2,...sn)factorial(n)logfactorial(n)logistic(t)logit(p)gamma(x)loggamma(x)beta(z,w)erf(x)erfc(x)binomial(n,k)multinomial(n1,n2,...nn)

ContinuousProbabilityDistributionsUniformDist(x,a,b)TriangularDist(x,m,w)Triangular3Dist(x,m,w1,w2)TriangularEnd3Dist(x,m,a,b)NormalDist(x, , )LognormalDist(x, , )ExponentialDist(x, )GammaDist(x, , )

WeibullDist(x, , )BetaDist(x, , )Beta4Dist(x, , ,c,d)CauchyDist(x, , )LaplaceDist(x, , )ExtremeValueDist(x, , )ParetoDist(x,a,b)ChiSquareDist(x, )StudentTDist(x, )FDist(x, 1, 2)

DiscreteProbabilityDistributionsSingleDist(k,c)DiscUniformDist(k,a,b)BernoulliDist(b,p)BinomialDist(k,n,p)PoissonDist(k, )HypergeometricDist(k,n,s,N)NegBinomialDist(k,n,p)GeometricDist(k,p)LogarithmicDist(k,p)MultinomialDist(bc,n,k1,p1,k2,p2,...km,pm)NoisyOrDist(e,leak,b1,p1,b2,p2,...bn,pn)NoisyAndDist(e,inh,b1,p1,b2,p2,...bn,pn)NoisyMaxDist(…)NoisySumDist(…)

Netica-WebNetica-WebisthenewestproductintheNeticafamily.ItisasystemtodeployyourBayesnetsovertheinternetasaquestion-answersystem.Suchasystemaskstheuserquestions,orprovidesadashboardtoenterrelevantinformation,andpresentstheuserwithconclusions.Ateachstageoftheprocess,thesystemchoosesthebestquestionstoaskbasedonthepreviousanswersgiven,usingNetica'ssensitivityanalysis.Itmaycontinuouslyprovideconclusions,orwaituntilitreachesacertainlevelofconfidencebeforepresentinganyinformation.ContactNorsysforfulldocumentationandpricinginformation(althoughyoumaytryitoutnowasdescribedbelow).

Howto:WithNetica-Web,youcaneasilybuildaninteractivewebsite,alsoknownasaHEDsystem(Human-ElectronicDialog).YouconstructaBayesnetinthenormalmannerusingNeticaApplication,andthenwithasingleclickofabutton,awebsiteisgenerated.First,selectanodeofinterest(calledaTargetnode),thenchooseNetica→BuildWebsite.Alternatively,youcanright-clickonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundandchooseHEDSystem→AddNettoWebsite.Inamomentyourbrowsershouldspringupwithyourworkingsystem.Youcancopy/pastetheURLfromyourbrowsertopublishyoursitetotheworld.Examplesite

Applications:Netica-Webcanbeusedtobuilddiagnosticsystems,suchastroubleshootingforsomemachineryorplant,ortoprovidemedical,environmental,corporate,etc.diagnostics.Itcanbeusedtobuildsystemsthatidentifysomeparticularitem(s)fromalargesetbasedonindirectcriterion,suchasaproducttobepurchasedfromaninventory,amovieorsongselection,restaurantchoice,person,etc.Itcanbuildclassificationsystemstodeterminewhichgroupanitemfallsinto,basedonitscharacteristics,suchasthepersonalitytypeofaperson,probablevotingpatterns,creditworthiness,whetheraplantorproductispoisonous,etc.Althoughthesearetypicalapplications,anyBayesnetcanberunonNetica-Web.

Netica-WebversusDecisionTrees:Netica-Webissuperiortooldtree-basedmethodsbecauseitiseasiertobuildandmaintainaBayesnetthanadecisiontree.Bayesnetsrepresenttheirknowledgeinaformwhichiseasyto

understand,andwhichcancombinehumanexpertisewithlearningfromdata.Furthermore,theirmodularityallowscombiningsub-modelsintoacompletemodel.Anychangesinprobabilitydistributionscandrasticallyalterthestructureoftheoptimumdecisiontree,whilsttheyproduceasmallchangeinaBayesnet.Bayesnetsallowuserstoskipquestions,answer“unknown”,orprovidelikelihoodanswers,andstillmaintainoptimalperformance.Andtheycanrecoverfromincorrectanswers,whichoftenthrowdecisiontreesonthewrongtrack.

ConstructingNetsforNetica-Web:WhenconstructingtheBayesnet,itsnodesaredividedinto(possiblyoverlapping)groups:observable,targetandintermediate.Eachobservablenodebecomesapotentialquestioninthesystem,andeachtargetnodewillresultinananswer,orhaveitsprobabilitiesdisplayed.Netica-Webdetermineswhichquestionsarethemostrelevanttodeterminethevaluesofthetargetresults.Itthenpresentsthosequestionsfirst,eitheroneatatime,orafewatatimeinascrollinglist(dependingontheconfigurationyouset).Theusermayskipquestionsatanytime,inwhichcasethequestionsaremovedtoanotherpartofthescreen,toallowlateransweringifdesired.

Sinceonlythemostrelevantquestionsareasked,basedonthepreviousanswers,aHEDsessionhasthefeelofaninteractivedialog,ratherthanjustfillingoutaform.Sincethesystemissojudiciousinchoosingwhichquestiontoaskfromitspoolofpossiblequestions,itisokaytohaveaverylargesetofpossiblequestions,furtheraddingtoitsabilitytoreachgoodconclusions.

AworkingHEDsystemcanbebuiltfromaregularBayesnetwithasingleclick,(Network→BuildWebsite)althoughifyouwanttoyoucanhighlycustomizeit.Itsvisualappearance,dimensions,colors,behavior,etc.canallbeeasilychanged,andgraphicscanbeaddedsothatitisseamlesslyintegratedwithalargerwebsite.

Hosting:YourHEDsystem,builtasdescribedabove,isbeinghostedbyNorsys,butifforsecurityorotherreasonsyouwishtohostityourself,thatisalsoanoption.Eitherway,ifyouwish,itcanbecomepartofyourexistingwebsite.Alternately,the“webpage”canjustbelocaltothemachineitisrunningon,allowingyoutodistributeyoursolutionasadesktopapplicationthatdoesnotrequiretheinternet.

TobuildyourfirstHEDsystem,besureyouhaveNetica5.0orlaterinstalled

onyourmachineandreadtheNetica-Webmanual.

Formoreinformation,emailNorsys.

Geo-NeticaManyNeticausershave,forsometimebeenusingNeticainconjunctionwithGIS(GeographicInformationSystems),sowedecidedtomakeiteasierforyou.

TheresultisGeo-Netica,ourlatestNeticaproduct,whichbringsBayesnetstothe2DworldofGIS.

Thisproductisinitsearlystages,butsinceitisalreadyveryusefultosome,wehavedecidedtomakeitavailableforsaletoselectclientsnow,withtheideathattheyareentitledtonewupgradesasfeaturesareadded.Additionally,wewilllistencloselytoearlyclients,todecidewhichnewfeaturestoadd.

Currentlyit:

-Operatesonrasterdata,suchasrasteroutputfilesfromArcGIS.-WorksinsideNeticawindow.-ShowsmultipleinputandoutputGISimagesatdesiredresolution.-Allowsprocessingatlowerresolutionforquickexplorationandmodelbuildingbeforedoingafullresolutionprocessing.

-CanclickonanypointwithinanimagetoenterdatafromthatlocationfromeachoftheimagesintotheBayesnettoseehowtheBayesnetprocessesit.

-Canhovercursoroverimage,todisplaydataonthatpoint.-Canauto-discretizenodesbasedonimagedata.-CandirectlyinteractwiththeBayesnetoneachprocessingcycle,forquickwhat-ifanalysis.

-Canhandleinputimagesthatarenotexactlythesamelocation,anddifferentresolutions.

-WorkswithanyBayesnetmodel,includingoneswithequations,probabilistictables,learnedfromdata.

-Bayesnetcouldbeforprediction,classification,diagnosis,probabilisticprocessing,speciesmodels,watermanagement,etc.

-Exampleinputimagesareelevation,slope,aspect,groundvegetation,speciespopulation,water,climate,rainfall,soils,satelliteimages,

traversability,friend/foepositions,municipalzoning,buildingtype,populationdensity,pollutantlevels,mineralassays,rocktype,accessibility,marketingdata,incomelevels,crimerates,propertycosts,politicalparty,etc.

Featurescomingsoon:-CanlearnBayesnetmodelsfromGISdata-EasierforBayesnetmodelstoincludedatafromotherpixelsneartotheonebeingoperatedon

Otherplannedfeatures:-Operateonvectordataaswellasrasterdata-InterfacenicelywithcommerciallyavailableGISsystems

IfyouareinterestedinpurchasingGeo-Netica,please=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">contactNorsys

Node-SetsSometimesitisusefultoform‘groups’or‘categories’ofnodes.WithNetica,youcancreategroupsofnodes,andtoassignanameandcolortoeach.Note:Arelatedconceptistogroupstatesofasinglenode.

Forinstance,toclearlyshowthedivisionsbetweenvariouspartsofyourBayesnet,youcanmakeeachsubsectionadifferentcolor.

Or,ifthereisasetofnodesthatyourepeatedlyuseforsomeoperation(forexample,asubsetofnodesthatyouoftenwanttoremovethefindingsfrom),youcansetthosenodesasanode-set.Wheneveryouwanttodotheoperation,youhaveNeticaselectthenodesinthatnode-set,andthenyouchoosetheoperationfromthemenu.

Anodemaybelongtoseveraldifferentnode-setsatonce,sointhatcaseNeticaneedsawaytochoosewhichnode-setcolortousewhencoloringit.Node-setshaveapriorityordering,soyoucanchoosethemostimportantcriteriatouseincoloringthem,whichyoumaywanttochangefromtimetotimetoviewthenetindifferentways.

Thenode-setoptionsare:

•CreatingNode-Sets•AddingandRemovingNodesfromNode-Sets•NodeColoring•UsingNode-SetstoSelectNodes•Node-SetReporting

CreatingNode-SetsIfthereisaparticularsetofnodesthatyouworkwithfrequently,youcanselectthemallandgivethemaname,creatinganode-set.AtanytimeduringyourworkyoucanselectthissetquicklybypressingtheCTRL+SHIFT+Sbuttonssimultaneously,andenteringthename.

Therearetwowaysnode-setsarecreated:

1.ByUser:Selectthenode(s)youwantinaparticularnode-set,chooseModify→SetNodeSet→New,(theshortcutkeyforthisisCTRL+SHIFT+N)andenterthenameofthenewset.Node-setnamesmustfollowtherulesofan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDname.Afteranode-setisset,youcanlateraddorremovenodesfromit.

2.Built-In:Automaticallybuilt-indefinition,basedonintrinsicqualitiesofthenodes.Thesenodesaredenotedwithadashinfrontofthename(e.g.–ConstantValue).

Thefollowingisalistofthebuilt-innode-sets,inorderoftheirpriorityforcoloring(LikelihoodFindinghighestpriority,Findingsecondpriorityetc.)

LikelihoodFinding Finding Deterministic

Boolean TwoState Discrete

Continuous Nature Title

Documentation ConstantValue Constant

DecisionSolved Decision Adversary

Utility Equation HasTable

Parentless Childless Node

Note:Someofthesenode-setswon’talwaysappearintheNodeSetPropertiesdialogbox.Toaccessthem,chooseModify→SetNodeSet→New,andtypeinanamefromtheabovelist(rememberingtobeginthenamewithadash).

AddingandRemovingNodesfromNode-SetsAsyouworkwithyournet,youmaywanttoaddorremovenodesfromapreviouslycreatednode-set.UnlikeaddingandremovingnodesfromyourBayesnet(whichcouldaffectthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">cpts),addingandremovingnodesfromanode-setwillonlyaffectthecategorizationofthenode(s)withinthenet.

Adding:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">Selectthenode(s)youwishtoaddtotheset,chooseModify→AddNodestoSet,andclickonthenameofthedesirednode-set,orclickonEnterandtypeinthename.Alternately,youcanselectoneormultiplenodes,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickontheselectionandchooseAddToNodeset.

Ifyouright-clickanunselectednode,themenuwilljustcontainNodesetinsteadofAddToNodeset,RemoveFromNodesetandSetNodeset,whichallowsyouto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_toggle_menu.htm');returnfalse;">togglewhetherornotthenodeclicked-onisinthenodesetyouchoose.

Removing:Selectthenode(s)youwishtoremovefromtheset,chooseModify→RemoveFromNodeSet,andclickonthenameofthedesirednode-set,orclickonEnterandtypeinthename.

Alternately,youcanuseright-clickingtoremovetheminamannersimilartothatdescribedaboveforadding.

Node-SetDialogBoxIfanode,ornodes,havepreviouslybeencreatedasanode-set,theycanbeassignedacolor.Coloringnode-setscanbeveryhelpfulvisuallywhenworkingwithaBayesnet,andisoneofthestyleoptionsavailableforimprovingthepresentationandcomprehensionofanet.

HowTo:ChooseModify→NodeSetProperties(fromtheoverheadmenuorby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthenet=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">background)Thesubsequentdialogboxcontainsalistofallthenode-setscreatedwithintheBayesnet.

Usingthisdialogboxyoucan:

SetColor:Beforeacolorhasbeenassignedtoauser-definednode-set,anXwillappearinthecolorswatchboxnexttoitsname.Tochooseorchangethecolorofanode-set,clickonitandclickSetColor.Acolorpalettewillbedisplayedfromwhichyoucanmakeyourchoice.ClickOkaytodismissthepalette,andthenclickApplyorOkayintheNodeSetpropertiesdialogbox.Youcanalsochangethedefaultcolorfortheothernodesofyournetatthistime.

NoColor:Toremovethecolorofanode-set,clickonit,thenclickNoColor.TheXthatwillappearinit’scolorboxindicatesthatthisnode-sethasnoassignedcolor,andwhenNeticaischoosingacolorfornodes,itwillskipthisnode-setandmovedowntothenextnode-setinthelist.Torestorethenode-set’spreviouscolor,clickonitandclickSetColor.Thelastchosencolorisremembered;henceyoucanjustclickOkayinthecolorpalettewhichappears.

ChangePriorityofColorDisplayed:Ifanodebelongstomorethanonenode-set,thefirstnode-setlistedinthePropertiesdialogboxwilldeterminethecolordisplayed.Tochangethecolordisplayed,dragthenode-settitleupordownthelisttothedesiredposition.

Rename:Tochangethenameofanode-set,selectit’snameandclick

Rename.Typethenewnameintothedialogboxthatappears.

DeleteNode-Set:Todeleteanode-set,clickonit’snameandpresstheDELETEkey.

SelectingNodesinaNode-SetTorestrictanoperation(e.g.clearing/settingfindings,removingtables,copyingnodes,absorbingnodes,modifyingnodekindordiscretization,hiding,etc.)toalimitedsetofnodes,youoftenselectthemfirst.Ifyouhaveacertainsetofnodesthatyouoftendoanoperationon,itisusefultocreateanode-setofthem,sothateachtimeyoucanquicklyselectthenodesinthatnode-set.

Torestrictanoperation(e.g.compiling,absorbingnodes,reversinglinks,oroptimizingdecisions)toapreviouslycreatednode-set,youcanquicklyselectthenodeswithinit.

HowTo:ChooseEdit→SelectNodes→InNodeSet,andthenselectthedesirednode-setfromthelistofnames,orEnterthename.TheshortcutkeyforthiscommandisCTRL+SHIFT+S.

Oncetheselectionhasbeenmade,itwillbehavelikeanyothernodeselection.

Thereisanalternatewaytoconsistentlyselectacertaingroupofnodes,ifallthosenodeshavethesamekeywordintheirtitleordescription(andothernodesdon't).FirstuseEdit→Findtoenterthekeyword,thenuseEdit→FindAlltoselectthemall.

Node-SetReportingUndertheReportmenuisaNodeSetsoption.Usethisfunctiontogenerateareportshowingallnodeswithinapreviouslycreatednode-set.

HowTo:ChooseReport→NodeSets→Alltogenerateadetailedlistofallthenode-sets.Ifyouwantareportonaspecificnode-set,chooseReport→NodeSetsandclickonthedesirednode-setname,oronEntertolabelasetofnodesforthereport.

Tohaveallthenodesofeachnode-setappearononeline,firstchooseReport→HorizontalFormat.Ifpastingthelistintoatableorcell,youmayalsowanttochooseReport→TabSeparators.

DynamicBayesNetsDynamicBayesnetsarealsoknownasDBNsortemporalBayesnets.TheyallowyoutospecifyaBayesnetmodelwhichhas"=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_time_delay_link.htm');returnfalse;">timedelay"links,indicatingthatthevalueofthechildnodedependsonthevalueoftheparentatanearliertime.LateryouexpandtheDBNsothatsomenodesintheoriginalnetbecomeseveralnodesintheexpandednet,indicatingthevalueofthatvariableatdifferentpointsintime.

DBNscanhavedirectedcycles,aslongasthereisadelaylinksomewherealongeachcycle.Delaylinkscanbeusedtomodelfeedback.Onceitisexpanded,itwillnolongerhavecyclesordelaylinks.

WeimproveNetica'sDBNcapabilitywitheachrelease,soifyouareworkingwithDBNsyoushoulduseatleastversion5.02.Downloadlatestversionsfromourftpsite.

ItisusuallyeasiesttoworkthroughanexampleDBNfirst.TheBayesnetcalled"Bouncing",inNetica's“=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examples”folder,issuitableforthatpurpose.

StepsforworkingwithaDynamicBayesNet:

1.CreateDBN2.Generatetimeexpansion3.Compileanduse

IfyouhaveanyrequestsorsuggestionsforNetica'sDBNfeature,besureto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">contactoursupportteam,sinceweareactivelyimprovingthisfeature.

SeealsoDBNBouncingExample

UsingDynamicBayesNets1.CreateDBN2.Generatetimeexpansion3.Compileanduse

NeticahasuniqueDBNcapabilitiesnotavailablewithanyothersoftware.Differentlinksmayhavedifferenttimedelays,sothatwhenthenetworkisexpanded,timeslicesmayhaveadifferentstructurefromeachother.Intheexpandednet,NeticawillreplicatenodesatafrequencythatisappropriatetomodelthedynamicsituationmodeledbytheDBN.Somenodeswillappearonlyonceintheexpandednet(correspondingtovariableswhosevaluesdon'tchangeovertime),somenodeswillappearafewtimes(forslowlychangingvariables),andotherswillappearmanytimes(forquicklychangingvariables).

Whenenteringthedelayamountforalink,youcanenteranumber(mostcommonissimply1),orthevalueofaconstantnode,oranequationbasedonthevaluesofoneormoreconstantnodes.Linkswithtimedelaysaredisplayedinareddish-browncolor.

Tosetthetimedelayofseverallinkstothesamevalue,selectthelinks,andchooseModify→DelayLinks,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clicktheselectionandchooseDelay.Youwillthenhavethechancetoenterthedelayyouwouldlikethemalltohave.Ifyoumakethedelay0,theywillbecomeregularlinks.

Anotherwaytosetlinkdelaysisfromanodepropertiesdialog.ChooseDelayfromthemultipurposeselectoratthebottom,andyoucanenteradelayamountforeachlinkenteringthenode.

>>Nextstep

UsingDynamicBayesNets1.CreateDBN2.Generatetimeexpansion3.Compileanduse

GenerateatimeexpandedversionofthenetbychoosingNetwork→ExpandTime.

Thiswillmakeanewwindowwithanewnetinit.Youwillprobablywanttoresizethiswindowtomakeitwider.

ThenewnetisaregularBayesnetwitheachPositionandVelocitynoderepresentingthepositionandvelocityatanewpointintime,withnodestotherightcorrespondingtolatertimes.

Prevstep<<>>Nextstep

UsingDynamicBayesNets1.CreateDBN2.Generatetimeexpansion3.Compileanduse

CompiletheBayesnetforprobabilisticinferencewithNetwork→Compile.Turnonautomaticupdating,ifitisn’talready,bytogglingNetwork→AutomaticUpdating,sothemenuitemischeck-marked.Experimentwithsettingthepositionorvelocity(byclickingonthedesiredinterval)toindicateobservationsatcertaintimes,andseehowthebeliefsforpositionandvelocityatallothertimeschange.

Youcanalsotry=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteringsomenegativefindingsbyholdingdowntheSHIFTkeywhenyouclickontheinterval.

Rememberthatthenumericalresultswillnotbeexact,duetothediscretizationandsamplingerrorinconvertingtheequationstoprobabilitytables.YoumayalsowanttotryafinerdiscretizationbychangingtheDiscretizationoftheoriginalunexpandednet.

Prevstep<<

TestingaNetUsingCasesThissectiondocumentsthemenuchoiceCases→TestNetUsingCases(or"Network→TestUsingCases"onolderversionsofNetica).ThepurposeofthisfeatureistogradeaBayesnetusingasetofrealcasestoseehowwellthepredictionsordiagnosisofthenetmatchtheactualcases.Itisnotfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetworks.

First,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenodesyoudonotwishthenetworktoknowthevalueofduringitsinference.Forexample,ifthenetworkisformedicaldiagnosis,youmightselectthediseasenodesandnodesrepresentingotherunobservableinternalstates.Wewillcallthesenodesthe"unobserved"nodes.ThenchooseNetwork→TestWithCases.Youwillbeaskedwhichfileofcasestouse,andafteryouchooseone,Neticawillstartprocessing.

The=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowwillcometothefrontanddisplaythepercentageofcasesprocessedsofar.HolddownCTRL+ALT+LEFTBUTTONatthesametimeifyouwanttostopprocessingcases(theresultsforthecasesalreadyprocessedwillthenbeprinted).Neticawillpassthroughthecasefile,processingthecasesone-by-one.Neticafirstreadsinthecase,exceptforanyfindingsfortheunobservednodes.Itthendoes=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingtogeneratebeliefsforeachoftheunobservednodes.Itgoesbackandchecksthetruevalueforthosenodesassuppliedbythecasefile(iftheyaresuppliedforthatcase),andcomparesthemwiththebeliefsitgenerated.Itaccumulatesallthecomparisonsintosummarystatistics.

WhenNeticaisdone,itwillprintareportforeachoftheunobservednodes

(exceptconstantnodes).Typicallyyouareonlyinterestedinsomeofthem,soyoucanignoretherest.Thereportforanodenamed"SpkQual"(withnodetitle"Sparkquality"mightlooksomethinglikethis:

ForSpkQual:Sparkquality

Confusion:

.......Predicted......

goodbadvery_bActual

------------------------

25300good

221764bad

1319430very_bad

Errorrate=6.325%

ScoringRuleResults:

Logarithmicloss=0.2144

Quadraticloss=0.1099

Sphericalpayoff=0.9409

Calibration:

good0-0.5:0|0.5-1:0|1-2:0|2-5:

0|

5-80:49|80-95:87.5|95-98:95.7|

bad0-1:0|1-2:1.52|2-5:2.4|5-10:

5.17|

10-50:20|50-85:82.6|85-95:90|95-100:

100|

very_bad0-0.1:0|0.1-0.5:0|0.5-5:6.94|5-10:

9.33|

10-20:16.2|20-95:83.3|95-98:98.9|98-99:

100|

99-100:100|

Total0-0.1:0|0.1-0.5:0|0.5-1:0|1-2:

0.431|

2-5:2.5|5-10:6.28|10-15:10.9|15-20:

13.3|

20-50:30.1|50-80:81.5|80-90:86|90-95:

93.7|

95-98:97.6|98-99:100|99-100:100|

TimesSurprised(percentage):

.................Predicted

Probability...................

State<1%<10%>90%>

99%

----------------------

--

good0.00(0/312)0.00(0/614)6.86(14/204)

0.00(0/0)

bad0.00(0/225)1.98(13/657)0.00(0/69)

0.00(0/0)

very_bad0.00(0/216)3.32(12/361)0.25(1/399)

0.00(0/31)

Total0.00(0/753)1.53(25/1632)2.23(15/672)

0.00(0/31)

SectionsoftheReportConfusionMatrix&ErrorsScoringRuleResultsCalibration&TimesSurprisedTableQualityofTest

NOTES:

IfyouhaveanyfindingsenteredbeforechoosingNetwork→TestWithCasestheywillbetakenintoaccountduringallbeliefupdating(unlessthecasefilehasacolumnforthatnode).Neticawillwarnyouinthisevent,sothatyoudon'tobtainwrongresultsbyinadvertentlyleavingsomefindingsinthenetwork.Asituationinwhichyouwouldwanttoleaveafindinginthenetworkisifthenetworkisdesignedforabroaderclassofcasesthanthecasefile.Forexample,ifyouhaveanetworkdesignedtohandlepeopleofbothgenders(andithasa'gender'node),butthecasefilecontainsfemalesonly,youshouldenterafindingof'female'forthe'gender'nodebeforegradingthenetwork.

Ifthefindingsforthenon-unobservednodesofacaseinthecasefileareimpossibleaccordingtothenetwork,thenaninconsistent-findingserrormessagewillbedisplayed,thatcasewillbeignored,andprocessingwillcontinue.Ifthenetworkmakespredictionsfortheunobservednodesthatareinconsistentwiththecasefile,thenofcoursenoerrormessageswillbegenerated,thenetworkwillsimplybegradedmorepoorly(andhavealogarithmiclossofINFINITY).Dependingonyourapplication,anyofthemeasurescalculatedcouldbethemostvaluabletoyou.However,ifyouwantasinglenumbertogradeanetwork,andaren'tsurewhichonetopick,we

suggestthelogarithmicloss.Thisfunctionwillproperlysupporta'NumCases'columninthecasefile,ifoneispresent.

Aswellasgradinganetwork,thisfeaturecanalsobeusedtodeterminetheusefulnessofparticulartestsorfindingsinarealworldenvironment.Oftengroupsoffindingsortestscanhavequiteadifferentusefulnesswhenconsideredtogether,thanwhenconsideredone-by-one,andthisfeaturealsoallowsyoutoinvestigatesuchgroups.Byselectingextranodesinthefirststep,youcanmakesomepossiblefindingsfromthecasefileunavailabletothenetwork.Thenyoucanseehowmuchtheresultsofthenetworkaredegradedbynothavingaccesstothosefindings.Inthemedicalexamplementionedearlier,youmightadditionallyselectthenodes'BloodTest'and'SmearTest',andthencomparethenewconfusionmatrixgeneratedwiththeoldone,tofindifthenumberoffalsenegativesandfalsepositivesofseriousdiseaseschangedsignificantly.

Thisfeatureisalsoavailabletoprogrammersusing=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPI;=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">contactNorsysformoreinformation.

TheConfusionMatrixConfusionMatrix:ThefirstpartoftheTestNetwithCasesreportisaconfusionmatrixtitled"Confusion:"ThepossiblestatesofSparkQualityaregood,badandvery_bad.Foreachcaseprocessed,Neticageneratedbeliefsforeachofthesestates.Themostlikelystate(i.e.theonewiththehighestbelief)waschosenasitspredictionforthevalueofSparkQuality.

ThiswasthencomparedwiththetruevalueofSparkQualityforthatcase,providingthecasefilecouldsupplyit.Theconfusionmatrixsuppliesthetotalnumberofcasesineachofthe9situations:(Predicted=good,Actual=good),(Predicted=bad,Actual=good),etc.Ifthenetworkisperformingwellthentheentriesalongthemaindiagonalwillbelargecomparedtothoseoffofit.

ErrorRate:Thenextpartofthereportis"Errorrate=6.325%".Thismeansthatin6.325%ofthecasesforwhichthecasefilesuppliedaSparkQualityvalue,thenetworkpredictedthewrongvalue,wherethepredictionwastakenasthestatewithhighestbelief(sameasfortheconfusionmatrix).

OthersectionsoftheTestNetwithCasesReport:ScoringRuleResultsCalibration&TimesSurprisedTableQualityofTest

ScoringRuleResults&LogarithmicLossValuesScoringRuleResults:ThethirdsectionoftheTestNetwithCasesreportistitled"ScoringRuleResults:"Thisdoesn'tjusttakethemostlikelystateasaprediction,butratherconsiderstheactualbelieflevelsofthestatesindetermininghowwelltheyagreewiththevalueinthecasefile.Theseresultsarecalculatedinthestandardwayforscoringrules.

Formoreinformationseeanyreferenceonscoringrules,suchas:

Morgan,M.GrangerandMaxHenrion(1990)Uncertainty:AGuidetoDealingwithUncertaintyinQuantitativeRiskandPolicyAnalysis,CambridgeUniv.Press,NewYork.

Pearl,Judea(1978)"Aneconomicbasisforcertainmethodsofevaluatingprobabilisticforecasts"inInternationalJ.ofMan-MachineStudies,10,175-183.

Logarithmiclossvalueswerecalculatedusingthenaturallog,andarebetween0andinfinityinclusive,withzeroindicatingthebestperformance.Quadraticloss(alsoknownastheBrierscore)isbetween0and2,with0beingbest,andsphericalpayoffisbetween0and1,with1beingbest.

Theequationsare:

Logarithmicloss=MOAC[-log(Pc)]

Quadraticloss=MOAC[1-2*Pc+sum[j=1to

n](Pj^2)]

Sphericalpayoff=MOAC[Pc/sqrt(sum[j=1ton]

(Pj^2))]

wherePcistheprobabilitypredictedforthecorrectstate,Pjistheprobabilitypredictedforstatej,nisthenumberofstates,andMOACstandsforthemean(average)overallcases(i.e.allcasesforwhichthecasefileprovidesavalueforthenodeinquestion).

OthersectionsoftheTestNetwithCasesReport:ConfusionMatrix&ErrorsCalibration&TimesSurprisedTable

QualityofTest

Calibration&TimesSurprisedTablesCalibrationTable:ThenextpartoftheTestNetwithCasesreportisatabletitled"Calibration:".Itindicateswhethertheconfidenceexpressedbythenetworkisappropriate(i.e."wellcalibrated").Forinstance,ifthenetworkwereforecastingtheweather,youmightwanttoknow:Ofallthetimesitsaid30%chanceofrain,whatpercentageoftimesdiditrain?Iftherewerelotsofcases,theanswershouldbecloseto30%.

Foreachstateofthenodethereareanumberofitemsseparatedbyverticalbars(|).EachitemconsistsofaprobabilitypercentagerangeR,followedbyacolon(:)andthenasinglepercentageX.ItmeansthatofallthetimesthebeliefforthatstatewaswithintherangeR,Xpercentofthemthetruevaluewasthatstate.

Forinstance:

rain0-10:8.5|

meansthatofallthetimesthebeliefforrainwasbetween0and10%,8.5%ofthosetimesitrained.Thereasonthattheprobabilityrangesareuneven,anddifferentfromstatetostate,andruntorun,isthattheyarechosensothattheXpercentagesarereasonablyaccurate.Thebinsizeshavetoadapt,ortheremightnotbeenoughcasesfallinginthatbin.Themorecasesyouprocess,themorefinewillbetheprobabilityranges.

Calibrationresultsareoftendrawnasagraph(knownasa"calibrationcurve")whereidealcalibrationisastraightdiagonalline.Formoreinformation,seeatextwhichdiscussesprobability"calibration"forexample,Morgan&Henrion90,p.110.

TimesSurprisedTable:Followingthecalibrationtableofthereportisthe"TimesSuprised"table.Itisusedtodeterminehowoftenthenetworkwasquiteconfidentinitsbeliefs,butwaswrong.Therearecolumnsforbeing90%confidentand99%confident(i.e.beliefsaregreaterthan90%or99%respectively),andalsoforbeing90%and99%confidentthatthevalueofthenodewill_not_beacertainstate(i.e.beliefsarelessthan10%or1%respectively).

Theratiosindicatethenumberoftimesitwaswrongoutofthenumberoftimesitmadesuchaconfidentprediction,andapercentageisalsoprinted.If

thenetworkisperformingwellthesepercentageswillbelow,butkeepinmindthatitisveryreasonabletobewrongwithaparticular10%or90%prediction10%ofthetime,andtobewrongwithaparticular1%or99%prediction1%ofthetime.Ifthenetworkrarelymakesstrongpredictions(i.e.beliefsarerarelycloseto0or1),thenthesemostoftheseratioswillbe0/0.

OthersectionsoftheTestNetwithCasesReport:ConfusionMatrix&ErrorsScoringRuleResultsQualityofTest

QualityofATestQualityofTest:ThefinalsectionoftheTestNetwithCasesreportisthe"QualityofTest"tableforbinarynodes,or"TestSensitivity"tablefornodeswithmorethan2states.Theseareusefulwhentheoutputofthenetworkisgoingtobeusedtodecideanaction,withoneactioncorrespondingtoeachstateofthenode.

Asamedicalexample,thenodemaybe"Disease-A"andhavethetwostates"Present"and"Absent".If,afterupdatingforacase,thenetworkreports"Present",thenaparticulartreatmentwillbestarted,butifitreports"Absent"thenthetreatmentwon'tbestarted.Thequestionis,atwhatprobabilityfor"Present"shouldwesaythatthenetworkisreportingPresent?Theconfusionmatrixanderrorratediscussedaboveweredeterminedusingthemaximumlikelihoodstate(i.e.theonewithhighestbeliefafterupdating).

Forabinaryvariable,thismeanschoosingthefirststateonlyifitsbeliefishigherthan50%.Butifeachstatehasadifferentcostofmisclassification,youmaynotwantthecutoffprobabilitytobe50%.Inthemedicalexample,itmaybedisastroustonottreatapatientwhohasthedisease,butnotthatseriousifheistreatedunnecessarily.Soyouwouldlikethenetworktoreport"Present"iftheprobabilityofthediseaseisabovesomesmallnumber,like2%.Itisamatteroftradingofftherateoffalsepositivesagainsttherateoffalsenegatives.Ideallyyouwouldjustconvertthenetworktoadecisionnetwork,byaddingadecisionnodefortheactiontobetakenandautilitynodeforthecostofmisclassification.However,atthetimethenetworkisconstructedandbeinggradedastoitsusefulness,theutilitiesmaynotbeknown.

TheQualityofTestsectionhasperformanceresultsforaseriesofcutoffthresholdprobabilities(whichrunverticallyinthefirstcolumn).Foreachcase,thebeliefsgivenbythenetworkareconvertedtoa"prediction".Thepredictionis"firststate"ifthebeliefforthefirststateishigherthanthecutoffprobability,and"secondstate"ifit'slower.Youmaywanttochangetheorderofthestates,sothatthefirststateisthe"positive"one,tobettermatchconventionalmeanings.

Themeaningsofthecolumnsare:

Sensitivity=Ofthecaseswhoseactualvaluewas

thefirststate,

thefractionpredictedcorrectly.

Specificity=Ofthecaseswhoseactualvaluewas

thesecondstate,

thefractionpredictedcorrectly.

PredictiveValue=Ofthecasesthenetwork

predictedasfirststate,

thefractionpredictedcorrectly.

PredictiveValueNegative=Ofthecasesthe

networkpredictedas

secondstate,thefractionpredicted

correctly.

OftenthisdataissummarizedwithagraphcalledtheROC(receiveroperatingcharacteristic)curve.TouseExcel(availablefromMicrosoft)tocreatetheROCcurvefromthisdata,selectthewholetable(exceptheadings)andwhileholdingdownthe<CTRL>key,typetcz.ThenopentheExcelfilecalled"Graph_ROC.xls"(availablefromtheNorsysftpsite),pasteintotheindicatedcell,andthegraphwillbedrawn.Ifthenodehasmorethan2states,insteadyouwillgetaTestSensitivitysection.Thefirstnumberofeach"column"isthecutoffthresholdprobability.Thesecondnumberofeachcolumnisthenumberofcaseswhoseactualvaluewasthestategivenatthelefthandsideoftherow,andwhichthenetworkcorrectlypredictedtobeinthatstate(i.e.itsbeliefwasgreaterthancutoffprobability),dividedbythetotalnumberofcaseswhoseactualvaluewasthatstate.

Itmayseemawkwardthatthecutoffprobabilitychangesinstrangesizedjumps.ThereasonisthatNeticaonlyreportsonvaluesforwhichitwasabletogatherenoughdata.Sorunningthetestusingagreaternumberofcasesgenerallyresultsinfinerdivisionsofthecutoffcolumn.

OthersectionsoftheTestNetwithCasesReport:ConfusionMatrix&ErrorsScoringRuleResultsCalibration&TimesSurprisedTable

SensitivityAnalysisNeticacandoextensiveutility-freesingle-findingsensitivityanalysis.Selectanode(calledthe"targetnode")andchooseNetwork→SensitivitytoFindingsfromthemenu.Areportwillbedisplayedinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowdisplayinghowmuchthebeliefs,meanvalue,etc.ofthetargetnodecouldbeinfluencedbyasinglefindingateachoftheothernodesinthenet(eachiscalleda"findingsnodes").

Thefirstpartofthereporthasasectionforeachfindingsnode,showinghowmuchitcaneffectthetargetnodeusingseveraldifferentsensitivitymeasures.Thesecondpartisasummarytablewhichcomparesthesensitivitiesforeachofthefindingsnodes.

Ifyouwanttolimitthereporttoafewfindingsnodes,firstselectthetargetnode,andthenuseCTRL-selecttoaddthedesiredfindingsnodestotheselection.ThenchooseNetwork→SensitivitytoFindings.

CurrentlythissensitivityanalysiswillonlyworkforBayesnetsandnot=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.

Example:Supposeyouareusingthenetfordiagnosis,andyouwanttodeterminewhichtestisgoingtoprovidethebestinformationaboutthepresenceofafaultordisease.SelectthenodeforthefaultordiseaseandchooseSensitivitytoFindings.Usethesummarylistofsensitivitiesattheendofthereportgeneratedtoidentifypossiblefindingsnodeswhichwillprovidethemostinformationaboutthefault/diseasenode.Ifyouwantmoredetailedinformationofhowthesefindingsnodescaneffectthefault/diseasenode,lookupeachoftheminthefirstpartofthereport.

SingleNumber:Ifyouwantasinglenumberwhichbestdescribesthedegreeofsensitivityofonenodetoanother,itisrecommendedthatyouusethefirstcolumnofthesummaryreportattheend.For=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousnodesornodeswith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">statevaluesdefined,thiswillbethevariancereduction,otherwiseitwillbethemutualinformation(i.e.entropyreduction).

Findings:Whenthesensitivitiesarecalculated,thefindingscurrently=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredintothenetwillbetakenintoaccount,whichcaneffectthesensitivitiessignificantly.

Forfulldocumentationonthisfunction,andeachofthesensitivitymeasurescalculated,seeSensitivitytoFindings.

SensitivityToFindingsOfsignificantimportanceinBayesnetworkisameasureoftheindependencebetweenvariousnodesofthenet.Usingjustthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructureand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_d_separation.htm');returnfalse;">d-separationrules,youcandeterminewhichnodesarecompletelyindependentofwhichotherones(seeEdit→SelectNodes→Info(D-)Connected),andhowthatchangesas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsarrive.However,dependenceisamatterofdegree,andusingNetica’ssensitivityfunctionsyoucanefficientlydeterminehowmuchafindingatonenodewilllikelychangethebeliefsatanother.

Duringdiagnosis,youmaywishtoknowwhichnodeswillbethemostinformativeincrystallizingthebeliefsofthemostprobablefaultnodes.Obviously,thatwillchangeasfindingsarrive,soitmayneedtoberecomputedateachstage.Inanetbuiltforclassification,youcandeterminewhichfeaturesarethemostvaluableforperformingtheclassification(i.e.“featureselection”).Inaninformationgatheringenvironment,youcanidentifywhicharethemostimportantquestionstoaskateachpoint(toprovideinformationonthevariablesofinterest),basedontheanswerstoquestionsalreadyreceived,soastoavoidaskingunnecessaryorirrelevantquestions.

Inreal-worldmodeling,suchasenvironmentalmodeling,youcandeterminewhichpartsofthemodelmostaffectthevariablesofinterest;therebyidentifyingwhichpartsshouldbemadethemostcarefullyandaccurately.

Selectanode(calledthe"querynode")andchooseNetwork→SensitivitytoFindingsfromthemenu.Areportwillbedisplayedinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">MessagesWindowdisplayinghowmuchthebeliefs,expectedvalue,etc.ofthequerynodewouldbeinfluencedbyasinglefindingateachoftheothernodes(eachiscalleda"varyingnode").

Thefirstpartofthereporthasasectionforeachvaryingnode,showinghowmuchitcaneffectthequerynodeusingseveraldifferentsensitivitymeasures.Thesecondpartisasummarytablewhichcomparesthesensitivitiesforeachofthevaryingnodes.

Ifyouwanttolimitthereporttoafewvaryingnodes,firstselectthequerynode,andthenuseCTRL-SELECTtoaddthedesiredvaryingnodestotheselection.ThenchooseNetwork→SensitivitytoFindings.CurrentlythissensitivityanalysiswillonlyworkforBayesnetsandnot=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetworks(i.e.networkswithdecisionnodes).

Hereisanexampleuseduringdiagnosis.HereisadescriptionofthemeasuresthatNeticacalculates.

SensitivityEquationsBelowaredescriptionsofeachoftheutility-freesensitivitymeasuresthatNeticacalculates.Firstaresomenotesforinterpretingthedescriptions.

Definition:Inthedefinitions,"belief"meansposteriorprobability(i.e.conditionedonallfindingscurrentlyentered).Inthenamesofthevariousmeasures"real"referstothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueofcontinuousnodes,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretenodeswhichhavearealnumericvalueassociatedwitheachstate"expectedvalue"meanstotaketheexpectationoveraquantity.

Range:Theminimumandmaximumvaluesthatthismeasurecantakeon.

Compare:Aquantitywhichisusefultocomparethevalueofthismeasureagainst(perhapstoexpressthismeasureasapercentage).

Equation:Notethatalltheconditionalsshouldincludeallfindingsalreadyenteredintothenetwork,soP(q)isreallyP(q|E),P(q|f)isreallyP(q|f,E),etc.

Notation:

Qisthequeryvariable

Fisthevaryingvariable

qisastateofthequeryvariable

fisastateofthevaryingvariable

Xqisthenumericrealvaluecorrespondingtostateq

SUM~qmeansthesumoverallstatesqofQ.Itappliesto

thewholeexpressionfollowing.

MIN~q,MAX~qaresimilartoSUM~q

E(Q)istheexpectedrealvalueofQbeforeanynewfindings

E(Q|f)istheexpectedrealvalueofQafternewfindingffornodeF

V(Q)isthevarianceoftherealvalueofQbeforeanynewfindings

H(Q)istheentropyofQbeforeanynewfindings

RMSis"rootmeansquare",whichisthesquareroot

oftheaverageofthevaluessquared.

MinimumBeliefDefinition:MinimumbeliefthateachstateqofQcantakeduetoafindingatF.Thisprovidesavalueforeachstate.

Range:[0,P(q)]P(q)ifQisindependentofF

Compare:P(q)

Equation:Pmin(q)=MIN~fP(q|f)

MaximumBeliefDefinition:MaximumbeliefthateachstateqofQcantakeduetoafindingatF.Thisprovidesavalueforeachstate.

Range:[P(q),1]P(q)ifQisindependentofF

Compare:P(q)

Equation:Pmax(q)=MAX~fP(q|f)

RMSChangeofBeliefDefinition:ThesquarerootoftheexpectedchangesquaredofthebeliefofstateqofQ,duetoafindingatFThisprovidesavalueforeachstate.ThisisthestandarddeviationofP(q|f)aboutP(q)duetoafindingatF,withthefindingatFdistributedbyP(f).

Reference:Spiegelhalter89&Neapolitan90,p394.Theycallthesquareofthisquantitysimply"variance".

Range:[0,1]0ifQisindependentofF

Compare:P(q)

Equation:sp(q)=sqrt(Vp(q))

Vp(q)=SUM~fP(f)[P(q|f)-P(q)]^2

"Variance"ofNodeBelief(named"QuadraticScore"inolderversionsofNetica)Definition:TheexpectedchangesquaredofthebeliefsofQ,takenoverallofitsstates,duetoafindingatF.

Reference:Spiegelhalter89&Neapolitan90,p394.Theycallthis"variance"(forthemitcomesoutthesameasVp(q)becausetheyjustuse2-statenodes).

Range:[0,1]0ifQisindependentofF

Equation:s2=SUM~fSUM~qP(q,f)[P(q|f)-P(q)]^2

MinimumRealDefinition:ThelowestthattheexpectedrealvalueofQcouldgoto,

duetoafindingatF.

Requires:NodeQiscontinuous,orhasrealnumberstatevaluesdefined.

Range:(-infinity,E(Q)]E(Q)ifQisindependentofF

Compare:E(Q)=SUM~qP(q)Xq

Equation:mmin=MIN~fE(Q|f)

MaximumRealDefinition:ThehighestthattheexpectedrealvalueofQcouldgoto,duetoafindingatF.

Requires:NodeQiscontinuous,orhasrealnumberstatevaluesdefined.

Range:[E(Q),infinity)E(Q)ifQisindependentofF

Compare:E(Q)

Equation:mmax=MAX~fE(Q|f)

RMSChangeofRealDefinition:ThesquarerootoftheexpectedchangesquaredintheexpectedrealvalueofQ,duetoafindingatF.Thisturnsouttobethesameasthesquarerootofthevariancereductionofexpectedvalue.

Requires:NodeQiscontinuous,orhasrealnumberstatevaluesdefined.

Range:[0,V(Q)]0ifQisindependentofF

Compare:E(Q)andmaybeV(Q)

Equation:sm=sqrt(Vm)

Vm=SUM~fP(f)[E(Q|f)-E(Q)]^2=Vr

VarianceReductionofRealDefinition:TheexpectedreductioninvarianceoftheexpectedrealvalueofQduetoafindingatF. ThisturnsouttobethesquareofRMSChangeofReal.

Requires:NodeQiscontinuous,orhasrealnumberstatevaluesdefined.

Range:[0,V(Q)]0ifQisindependentofF

Reference:Pearl88,p323.WhathesaysisC(T|X)isactuallyC(T|X)-C(T).

Varmapping:T->Q,X->F,C->V,t->qandXq

Compare:V(Q)

Equation:Vr=V(Q)-V(Q|F)=Vm

V(Q)=SUM~qP(q)[Xq-E(Q)]^2

V(Q|f)=SUM~qP(q|f)[Xq-E(Q|f)]^2

E(Q)=SUM~qP(q)Xq

EntropyReduction(MutualInformation)Definition:ThemutualinformationbetweenQandF(measuredinbits).TheexpectedreductioninentropyofQ(measuredinbits)duetoafindingatF.

Range:[0,H(Q)]0ifQisindependentofF

Reference:Pearl88,p321.HehassignofI(T,X)backwards.

Varmapping:T->Q,X->F,I(T,X)->I

Compare:H(Q)

Equation:I=H(Q)-H(Q|F)

=SUM~qSUM~fP(q,f)log(P(q,f)/[P(q)P(f)])

Notethatthelogisbase2,whichistraditionalforentropyandmutualinformation,sothattheunitsoftheresultswillbe"bits".

Sensitivity-DiagnosisExampleIfyouwanttodeterminewhichtestisgoingtoprovidethebestinformationaboutthepresenceofafaultordisease,selectthenodeforthefaultordiseaseandchooseSensitivitytoFindings.Usethesummarylistofsensitivitiesattheendofthereportgeneratedtoidentifypossiblevaryingnodesforwhichafindingwillprovidethemostinformationaboutthequerynode.Ifyouwantmoredetailedinformationofhowthesevaryingnodescaneffectthequerynode,lookupeachoftheminthefirstpartofthereport.

Ifyouwantasinglenumberwhichbestdescribesthedegreeofsensitivityofonenodetoanother,itisrecommendedthatyouusethenumbersprovidedinthefirstcolumnofthesummaryreportattheend.Forcontinuousnodes,ornodeswithrealnumberstatevaluesdefined,thiswillbethevariancereduction,otherwiseitwillbethemutualinformation(i.e.entropyreduction).

Whenyoudoacompletesensitivityreport(i.e.onlythequerynodeselected),theninthereportNeticaalsoshowsthesensitivityofthequerynodetoafindingatthequerynodeitself.Ofcourse,theminimumandmaximumbeliefsforeachstatewillbe0and1respectively,andthemaximumreductionsinvarianceandentropywillbe100%.Thisnodeisincludedinthereportforcompleteness,andtoquicklyseewhatthemaximumofeachsensitivityvalueis(forexample,whatthefullvarianceandentropyis).

Whenthesensitivitiesarecalculated,allfindingscurrentlyenteredintothenetworkwillbetakenintoaccount,whichcaneffectthesensitivitiessignificantly.

Ifyouaretryingtofindthenextbestobservationtomakeadiagnosis,youwillprobablywanttocombinethecostofeachpossibleobservationwithitsexpectedvalueasindicatedbythesensitivitytothatobservation(finding).

Ifyouwanttoconsiderpairsofobservations,ormultipleobservations,theresultscanbequitedifferentthanifyouconsiderobservationsoneatatime.Todoapairofobservations,youmustentereachpossiblefindingofthefirstobservation,anddoasensitivityanalysisonthesecondobservation,thenaveragetheresults(weightedbytheprobabilityofthefindingforthefirstobservation)tofindanexpectedvalue.

YouwillprobablyneedNeticaAPItoautomatethis.Thesensitivitymeasures

availablefromNeticaAPI,asofversion3.10,aremutualinformation(i.e.entropyreduction),andRMSchangeofreal(i.e.variancereductionofreal).

TransformingaNetTherearecertainwaysthatNeticacantransformanetmodelwhichmodifiesitsrepresentationwithoutmodifyingitsmeaning.Neticacanremovenodesandreversethedirectionoflinksinsuchawaythatanyinferencedonewiththeresultingnetyieldspreciselythesameresultsastheoriginalnet(exceptofcoursefindingscan’tbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredforremovednodes,andtheirresultingbeliefsareunavailable).

Somereasonstodothesetransformsareto:simplifythenet,applythenettomorespecificproblems,gainunderstandingofthenetoroftherealworldrelations,orputthenetinaformforeasierprobabilityorfunction=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probab_assessment.htm');returnfalse;">assessment.

LinkReversalsSupposePandCare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discreteor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizednodeswithinanet,andthatPisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentofC.SincethereisalinkgoingfromPtoC,thetableforthetwonodesisexpressedasprobabilitiesforthestatesofC,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionedonthestatesofP(orafunctionprovidingC’svalueintermsofP’svalueifthenodeisdeterministic).ButsometimesyoumightwanttoknowwhattheprobabilitiesforthestatesofPare,conditionedonthestatesofC.

Youcanachievethatbydoinganettransformknownaslinkreversal,whichreversesthelinkfromPtoC.Whenthatlinkisreversed,theotherlinksandthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofCandPareadjustedinsuchawaythatany=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">probabilisticinferencedoneafterthereversalwillyieldexactlythesameresultsasbeforethereversal.Inotherwords,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_joint_distribution.htm');returnfalse;">fulljointprobabilitydistributionofthenetdoesnotchangewhenalinkisreversed.Theglobalrelationshipbetweenthenodesremainsthesame;justthelocalexpressionsofithavebeenchanged(asisthecasewithnodeabsorption).

Linkreversalistheprobabilisticgeneralizationoffunctioninversion,andisagoodexampleofBayesruleinaction.

AddsLinks:Duringthereversal,NeticamayaddlinkstoCfromtheparentsofP,and/oraddlinkstoPfromtheparentsofC,whichwillincreasethecomplexityofthenet(alllinksaddedwillbeconfinedtoPandits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Markov_boundary.htm');returnfalse;">Markovboundary).Whenlinksareadded,thesizeofCPTsmaygrowsignificantly,andsometimesenormously.Thesizeofthetablesistheproductofthenumberofstatesofalltheparents,sothesizeofeachtablecangrowexponentially.Whenlinkreversalsresultinanodehavingmanyparents,theoperationmaybeslow,orNeticamayreportthatthereisnotenoughmemoryavailable.

RemovesLinks:Occasionally,duringareversal,NeticamayremovelinkstoCfromtheparentsofP,and/orremovelinkstoPfromtheparentsofC,resultinginasimplernet.Forexample,ifreversingalinkaddedotherlinks,thenreversingitagainwillremovethem(assumingallthenodeshavenondegenerateCPTs,andthattherearenomajorroundinginaccuracies).

SimplerNet:Usuallywhenanetissimplerduetothedirectionofitslinks,itprovidesabettermodeloftheworld.Forexample:itusuallyrepresentstruecausalitymoreaccurately,itmaybebetteratgeneralizing,andofcourseitallowsforfastercomputation.Sometimeslinkreversalscanbeusedtosearchformoresimplenets,givenanetthatwasoriginallylearnedfromdata.InthatcaseNeticamightnotalwaysautomaticallyremovelinksthatshouldberemoved,becausealthoughtheselinkswillbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_weak_link.htm');returnfalse;">weak,theywillnotbecompletelyineffectual(perhapsbecausetheprobabilitytableslearnedarenot“exact”).Youwouldhavetoremovetheseweaklinksbyhand.

HowTo:Toreversealinkyou=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_link.htm');returnfalse;">selectitandchooseModify→ReverseLinks,orclickthe toolbarbutton.Ifanodeis=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectedwhenyouclickthebutton,Neticawilldoallthelinkreversalsnecessarytomakealllinksinvolvingthenodepointtoit.Alternately,youcan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonalink,andchooseReversefromthemenu.Right-clickingonan__unselected__nodegivestheoptionsLinks→ReverseSoAllIncomingandLinks→ReverseSoAllOutgoing,whichwilldoallthereversalsnecessarytoachievethestatedeffect.Ifalllinksaremadetopointawayfromthenode,thenmanyextralinksmayhavetobeaddedbetweentheancestorsofthenode(notjustitsMarkovboundary),andNeticamayreportthatthereisnotenoughmemoryavailable.

SeveralLinks:Ifyouhaveseverallinkstoreverse,youcanselectthemall(e.g.byCTRL-clickingonthem),andthenclickthe button.Theamountoftimeandmemoryrequiredtoreverseasetoflinksdependsgreatlyontheorderinwhichtheyarereversed.Unlessyouknowagoodordertodothereversals,youshouldreversethemallatonceratherthanone-by-onesothatNeticacanchooseagoodordertodothem.

SeealsoDisconnectingandReconnectingLinks

NodeAbsorptionNodeabsorptionisanettransformwhichremovesnodesfromaBayesnetordecisionnet,andmakesanynecessaryadjustmentstotheresultingnet,sothatanyinferencedonewithityieldsthesameresultsasbeforethenodeswereremoved(exceptofcourseyoucan’tinteractwiththeremovednodes).Thelocalrepresentationischanged,buttheglobalrelationshipsarenotchanged(asisthecasewithlinkreversal).Inprobabilitytheorythisissometimeslooselycalled“summingoutavariable”.Itleavesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_joint_distribution.htm');returnfalse;">fulljointprobabilitydistributionoftheremainingnodesunchanged.

Asanexample,supposeyouhavealargenetthathasbeenconstructedovertimebyacombinationofexpertassistanceandprobabilitylearning.Itshowstherelationshipsbetweenhundredsofvariables,andcontainsmuchvaluableinformationthatcouldbeusedinanumberofdifferentapplications.

Nowyouwanttouseitinanapplicationwhereonly10ofthevariableswillbeofinterest.Ineveryqueryofthenewapplication,aparticular4ofthese10willalwayshavethesamefindings.Forexample,oneofthenodesintheoriginalnetmightbyGender,andintherestrictedapplicationthenetwillonlybeusedforfemales,soyouwouldliketo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enterapermanentfindingof‘female’fortheGendernode.Thesenodesarecalledcontextnodes.Ineachofthequeries,youwillbereceivingnewfindingsfor4othernodes,andthenyouwanttheresultingbeliefsoftheremaining2outof10.Thenodesthatwillalwayshavenewfindingsarecalledfindingsnodes,andthosewhosebeliefsyoumaywantarecalledquerynodes.Thehundredsofothernodesinthenetmightbeinvolvedinintermediatecalculations,butyoudon’tcareabouttheirvaluesexplicitly.

Youcansimplifythelargenetdowntoonewithjust6nodesusingnodeabsorption.Firstenterthepermanentfindingsforthecontextnodes.Thenselectallthenodestobeabsorbed(i.e.allthenodesexceptthefindingsand

querynodes),andchooseModify→AbsorbNodesorclickthe toolbarbutton.Theselectednodeswillberemoved,andsomelinksmaybeaddedand/orreversed.

Order:Ifyouwant,youcanabsorbthenodesafewatatime,byselectingeachgroupandclickingthe toolbarbutton.Thefinalresultofabsorbingasetofnodesisnotdependentontheorderinwhichtheywereabsorbed,butthetimeandmemoryrequiredmaybegreatlyaffected.Ifyouhaveasetofnodestoabsorbandyoudon’tknowagoodordertouse,thenitisbesttoabsorbthemallatonce,sothatNeticacanpickagoodorder.

Returningtotheexample,theresulting6nodenetwillgivethesameinferenceresultsastheoriginallargeone,fortherestrictedqueriesyouwillbemaking.Ifyouareguaranteedthattherewillalwaysbefindingsforeveryfindingsnode,thenyoucanfurthersimplifythingsbyremovinganylinksthatgofromfindingsnodePtofindingsnodeC,providingCdoesnothaveaquerynodeasaparent.Thismeansthatifyoucanreverselinkstomakealltheevidencenodesancestorsofallthequerynodes,thenyoucanremoveallthelinksbetweentheevidencenodes.Anyfindingsnodethatisleftcompletelydisconnectedbythisoperationisirrelevanttothequery,andcanbedeleted.Andnowyoucanexaminethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofthequerynodestoseedirectlyhowtheydependonthefindings.Youmayjustbeabletolookupthedesiredprobabilitieswithoutdoing=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingatall!

ComplexityDanger:Eventhoughareducednethasfewernodesthantheoriginal,internallyitmayactuallybemorecomplex,sometimesmuchmorecomplex,ifmanylinkswereaddedduringnodeabsorbingorlinkreversing(rememberthatthesizeofanode’sCPTcanbeexponentialinitsnumberofparents).Generallyspeaking,absorbingoutcontextnodes(i.e.nodeswithfindingsentered)whichhavemanyancestornodesresultsintheworstincreaseincomplexity.Thenextworstisabsorbingoutnon-contextnodes(i.e.nodeswithnofindings)whichhavemanydescendantnodes.Absorbingoutcontextnodeswithnoancestors,ornon-contextnodeswithnodescendants,willnot

addanylinks.Ofcourse,ifthenumberofqueryandfindingsnodesisverysmallandtheyhavefewstates,theresultingnetmustbeverysimple,althoughthetransformationstogenerateitmighttemporarilyrequirealotofmemory.

NetFragmentLibrariesOftentheprobabilistic=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationbetweenanodeandits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsrepresentsasmallpieceoflocalknowledgewhichmaybeapplicableinanumberofdifferentnetstobeusedindifferentsituations.Thatrelationmayhavebeenlearnedfromdata,orenteredbyanexpert.Eachnewnetthatitisplacedincapturestheglobalrelationsbetweensuchlocalpiecesofknowledge,andbeliefupdatingcombinesthelocalandglobalknowledgewiththedetailsofsomeparticularcase.

Youcankeeppiecesoflocalknowledgeasnetfragmentsinanetlibrary,andlaterpastethemintonetsyoudesigntosolveaparticularproblem.Hereisanexampleofafewnetfragmentsinalibrary:

Example:Forexample,supposethatyoumadeasimplenetconsistingofanodecalledForecastconnectedtoanodecalledWeather(whattheweatherturnedouttobeaftertheforecast).Youcouldputthelinkbetweenthemeitherway,sinceinthissituationyoucan’treallycapturecausation(theyarebothcausedbyothervariables,suchastheweatheratearliertimes),butsayyouputthelinkfromWeathertoForecastbecauseoftenitsbettertoputlinksfrommoreimmutabletolessimmutablevariables.Youcouldlearnitsprobabilitiesfromasetofcasesconsistingoftheforecastandwhattheweatherturnedouttobe.Thenyoucouldputitinalibrarywhereitmightlookliketheleftmostfragmentinthediagramabove.Later,yougraftitintonetsforinferenceinvolvingtheweatheranditsforecast,suchasthedecisionproblemexample:

Example:Asanotherexample,supposeyouhaveadeviceformeasuringtheflowrateinapipe.Itproducesbiasedreadingsdependingontheambienttemperature,anditcanmalfunctioninafewdifferentways,eachofthemproducingwrongorinaccuratereadings.Youcanmodelthedevicewitha4nodenet,consistingofonenodeforthereadingonthedevice,and3parentnodescorrespondingto:actualflowrate,ambienttemperature,anddevicestatus(okay,broken1,broken2,etc.).Youentertheprobabilitytable,andthenyoudisconnectthenodefromitsparentsandplaceitinalibrary.Therightmostnodeinthefirstdiagramonthispageshowshowitwillappear.

Later,ifyouhaveanettomodelasituationinwhichyouusetheinstrumenttomaketwomeasurementsoftheflowsintwoconnectedpipeslocatedinthesameroom,youjustduplicatethedevicecharacteristicsnodefromthelibrarytwiceintothenewnet,andgraftittotheappropriatenodesinthatnet,asshowninthediagrambelow.Notethatiftheambienttemperaturecouldbedifferentbetweenthetwomeasurements,thentheroom_tempnodewouldappearastwoconnectednodes,similartotheflownodes,andthesamegoesfortheinstrument_statusnodeifthedevicemayhavebrokenbetweenmeasurements.

DisconnectingandReconnectingLinksPurpose:Alinkmaybedisconnectedfromitsparentnode,withoutthelinkactuallybeingremoved.Thatmeansthatthechildnodecanmaintaintheinformationontheconditionalprobabilitytableithadwithitsparent,withoutactuallybeingconnectedtotheparent.Theintentionisthatlateritwillbereconnectedtotheparent,ormorelikelytosomeothernode,beforeitisusedforinference.Itmaybereconnectedsoonafterwards,orthenode(s)maybeplacedinalibraryofnetfragmentsandonlyreconnectedwhenthelibraryisusedtobuildanewBayesnet.

HowTo:Todisconnectsomelinks,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_link.htm');returnfalse;">selectthemandthenchooseModify→DisconnectLinksorclickthe toolbarbutton.Eachlinkwillturnintoashortstubconnectedtoitschildnode,andlabeledwiththenameofthelink.Ifyouhavenotpreviouslynamedthelinks,thenNeticawillnamethemwiththenamesoftheparentnodes.Ifyouwanttodisconnectallthelinksenteringsomenode(s),selectthenode(s)andchooseModify→DisconnectLinks.Youcanalsohiliteindividuallinks,right-clickandchooseDisconnect.

ByDragging:Ifyouwanttodisconnectalinkwhilemostlymaintainingitsshape,firstclickonthelinktoselectit.Thenclickdownonthehilitedboxattheendofthelink(theendwithoutthearrow),anddragitawayfromtheparentnode.Whenyoureleasethemousebuttonyouwillknowthatyouhavedraggedtheboxfarenoughifthenameofthelinkappearsbesideit.Allofthebendsofthelinkwillbemaintained.

ChildEnd:Alinkcannotbedisconnectedfromitschildnode.Thatwouldnotmakesense,sinceadisconnectedlinkisreallyjusta“parentplace-holder”tomaintainthenode’srelation(e.g.CPT)untilitisconnecteduptoanewparent.Toachievetheaffectofdisconnectingalinkatthechildend,itsometimesmakessensetodoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_reversal.htm');returnfalse;">linkreversal,andthendisconnectthelinkattheparentend.

Reconnection:Toreconnectadisconnectedlinktoanewnode,firstclickonthelinktoselectit.Itwillbeoutlinedwiththehilitecolor,andtherewillbeaboxofhilitecoloratthedisconnectedendofthelink.ChooseModify→ReconnectLinks.

Youmaydisconnectalinkfromoneparentandconnectittoanewparentinonemotionifyouwish.

SeealsoLinkReversals

SeealsoDeletingNodesandLinks

CreatingandUsingNetLibrariesCreating:Neticamakesiteasytomaintainlibrariesofdisconnectednodesandsubnets.Tomakeanewlibrary,justchooseFile→New→Networkorclickthe toolbarbutton.Librariesarehandledinternallyinthesamewayasregularnets.Nodesandsubnetscanbecopiedtoitby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingnodes(thereisnoneedtoselectlinks),andusingEdit→CopyandEdit→Paste,whichcantransfermaterial(nodes,linksand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTs)fromonenettoanother.Whenanodeisbeingduplicated,butoneofitsparentsisn’t,thentheduplicatednodewillhaveadisconnectedlinkwherethatparentwas.

Using:Tousenodesinthelibrary,youuseEdit→CopyandEdit→Pasteagain,thistimetoduplicatefromthelibraryintothenewnet.Thenyouconnectupanydisconnectedlinks,beforecompilingthenetorusingitforinference.

Example:Forexample,tocreatealibrarywithjustthe“instrument”nodeoffigure6.1,firstyouwouldmakeanetwiththe4nodes:flow_rate,temperature,instrument_statusandinstrument.Putlinksfromnodesflow,temperatureandinstrument_statustoinstrument.Enteraprobabilitytableforthenode“instrument”.NowmakeanewnetwithFile→New→Network,selectthe“instrument”nodeintheoriginalnet,doanEdit→Copy,clickinthenewnet,doanEdit→Paste,thenaFile→Save.Younowhavefilewhichisalibrarywithasinglenodeinit.

Atalatersession,youcanusethelibrarytoconstructanetinwhichtheinstrumentisusedtomeasuretheflowsasdescribedatthebeginningofthischapter.MakeanewnetwithFile→New→Network,addthenodesflow1,flow2,instrument_statusandroom_temp,linkthemtogetherasshowninfigure6.2,andentertheprobabilitytablebetweenthem.ThenuseFile→Opentoopenthelibraryfilewiththeinstrumentnode.Selectthatnode,doan

Edit→Copy,thenclickintheapplicationnetwhereyouwanttheinstrumentnodetoappear.DoanEdit→Paste,clickagainwheretheothercopyofitshouldbeanddoanotherEdit→Paste.Finally,hookupeachofinstrument’sdisconnectedlinkstotheirappropriatenodesusingthemethoddescribedintheprevioussection.

Nowtheapplicationnetisreadyforprobabilisticinference(youcandoaNetwork→Compilemenucommand).Perhapsyouhavepositivefindingsforthe“instrument”node(i.e.whatyoureadfromitsdial),andyouusethemtodetermineflowsandtheiruncertaintiesinawaythatproperlyaccountsforrandom(uncorrelated)andsystematic(correlated)errors,aswellasallthebackgroundknowledgeaboutthesituation.

NeticaAPI:Asasisterproduct,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaProgrammer’sLibrary(API)canbeusefulforautomatingtheprocessofconstructingnetsthatarecomposedofnodesorsubnetsfromalibrary,perhapsbyusingtemplatesorrules.

COMInterface–C#andVisualBasicProgrammingNeticahasAPIsforseveraldifferentcomputerlanguages(suchasJava,C/C++,etc.),whichallowittobeusedaspartofacomputerprograminoneofthoselanguages.Formoreinformation,seeNeticaAPI.

OnesuchNeticaAPIiscalledNetica-COM.YoucanprogramNeticathroughitsCOMinterface(alsoknownasActiveXorAutomation)usinganycomputerlanguagethatcanaccessaCOMinterface.ForexampleC#,VisualBasic(VB),COMenabledJava,orC++.ThebelowiswrittenasthoughVBisbeingused,butitpertainstoprogrammingintheotherlanguagesaswell.

AgreatbenefitofprogrammingNeticathroughitsCOMinterfaceisthatpeoplecaninteractwiththeGUIatthesametimeasyourVBprogramisrunning.Thatcanbeusefulfordebugging,demos,anddistributingproductsthattakeadvantageoftheNeticauserinterfacebyallowingtheend-usertointeractdirectlywiththeBayesnet.

IfyouhaveprogrammedanMSOfficeproductusingVisualBasic,youwillfindsomesimilaritiesinstylewiththeNeticaCOMinterface.

TouseNeticaCOMinitsfullyenabledform,youmusthaveaNeticalicensepasswordthatisforbothNeticaApplicationandNeticaAPI.First,runthelatestversion(mustbeversion3.10orgreater)ofNeticaApplication,soitcanregisteritselfintheregistry.IfyouhaveseveralversionsofNeticaonyourcomputer,theversionofNeticathatVBwillusewillalwaysbetheonethatwaslastrun(forexample,bydouble-clickingit).Youcanleaveitrunningorexitit.ThentogetaccesstoitfromVisualStudio,chooseProject→AddReferencefromVisualStudio,clicktheCOMtabifnecessary,andcheck-marktheentrycalled"Netica1.0ObjectLibrary"(withperhapssomeotherversionnumber).

YoucanthenusetheobjectbrowsertoseetheNeticaobjectsandfunctionsavailable.ChooseView→ObjectBrowserorView→OtherWindows→ObjectBrowser,andthen:

•InVisualStudio6,setthelibrarytoNeticaintheupperleftchoicebox.•InVisualStudio.NET,oneofthetoplevelentriesintheobjectbrowserwillbe"Interop.Netica".Youcanbrowsethat,butitwon'tbeasgoodasbrowsing

theNeticalibrarydirectly,becauseyouwon'thaveadescriptionforeachfunction.Ifthereisnoentryatthetoplevelforthelibrarynamedsimply"Netica"(withthebooksicon),clickontheCustomizebuttonatthetopofthewindow,andthentheAddbuttonofthedialogboxthatappears.ChoosetheCOMtab,selecttheNeticalibraryfromthelist,clickSelectandthenOkay.NowtheNeticalibraryshouldappear,andyoucanbrowseit.

Intheobjectbrowser,whenyouclickonanyfunctionorenum,thenashortdescriptionwillappear,whichisgoodenoughformostprogrammingwork.Ifyouneedmoredetail,thenyouwillnoticethatwithinthedescriptionisthenameoftheequivalentfunctionintheNetica-CAPI.YoucanlookupthatfunctionintheNetica-Cdocumentation.

•Toviewthatdocumentation,see:http://www.norsys.com/onLineAPIManual/index.html•Todownloadit,goto:http://www.norsys.com/download_api.html

ExampleCode:HereisexamplecodetoprogramNeticainC#,VisualBasicandManagedC++(C++/CLI)usingtheCOMinterface.ThereisalsoanexampleVisualStudioprojectforeach,called"NeticaDemoforxx"withinthe"Netica\Neticaxxx\ProgrammingExamples"folderoftheNeticadownloadpackage.

Password/Distribution:IfyourlicensepasswordenablesonlyNeticaAPI,thentheGUIwilloperateinalimitedmode,andifyourlicensepasswordenablesonlyNeticaApplication,thenyourVBcallstoNeticawilloperateinalimitedmode.IfyouwanttodistributeyourVBprogramthatusesNetica,youneedtoonlysendNetica.exe(andperhapsNetica.hlp),butnotNetica.dll.Makesureyouhavetherequiredlicensefrom=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsysbeforeyoudoso.

TostartupNeticasothatitoperateswithapasswordthatisnotputintheRegistry,startitfromyourVBprogramwiththecommandlineargument-passwordfollowedbythepasswordyouwantNeticatouse.Thatpasswordwillnotbeenteredintotheregistry,anditssecuritypartwillnotbevisibletotheuser.

GUIControl:YoucanusetheVisiblepropertyoftheNetica.Applicationobjecttodeterminewhetherornotthegraphicaluserinterface(GUI)ispresentornot(bysettingittotrueorfalse,seetheexamplebelow).Ifitisnotvisible,thenitwillbeaminimizedwindowappearingonlyasanicononthetaskbar.Ifyouwishtopreventtheuserfromun-minimizingit,therebypreventingthemfromhavingaccesstotheNeticaGUI,settheUserAllowedpropertyofNetica.Applicationtofalse.

Example:Todotheabove,yourprogrammighthaveapartlookingsomethinglikethis:

Shell("C:\\Netica\\Netica312\\Netica.exe–password+Me/MyOrg...")

DimappAsNewNetica.Application

app.Visible=False

app.UserAllowed=False

...

app.Quit

Continuous/DiscreteNodes:Tomakeacontinuousnode,useBNet.NewNodeandpass0forthenumberofstates.Tolaterdiscretizeit,orsetthelevelsofanalready=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenode,simplychangeitsLevelproperty.YoujustsetNode.Level(0),thenNode.Level(1),etc.Itwilladjustthenumberofstatesofthenodeeachtime.Ifyouhaveverymanystates,youmaywanttostartwiththehighestfirst,sincethatissomewhatmoreefficient.

C#ExampleCodeBelowisanexampleC#programthatdoesthesamethingasthe"Demo"programthatshipswithNeticaC-API.ThereisaVisualStudioprojectforit,called"NeticaDemoforC#"withinthe"Netica\Neticaxxx\ProgrammingExamples"folderoftheNeticadownloadpackage.(moreinfoonprogrammingNeticainC#)

usingSystem;

usingNetica;

namespaceNeticaDemo

{

classProgram

{

staticvoidMain(string[]args)

{

Console.WriteLine("WelcometoNeticaAPIforC#!");

Netica.ApplicationClassapp=newNetica.ApplicationClass();

app.Visible=true;

stringnet_file_name=AppDomain.CurrentDomain.BaseDirectory+"..\\..\\..\\ChestClinic.dne";

Streamerfile=app.NewStream(net_file_name,null);

BNetnet=app.ReadBNet(file,"");

net.Compile();

BNodeTB=net.Nodes.get_Item("Tuberculosis");

doublebel=TB.GetBelief("present");

Console.WriteLine("Theprobabilityoftuberculosisis"+bel.ToString("G4"));

BNodeXRay=net.Nodes.get_Item("XRay");

XRay.EnterFinding("abnormal");

bel=TB.GetBelief("present");

Console.WriteLine("GivenanabnormalX-Ray,theprobabilityoftuberculosisis"+bel.ToString("G4"));

net.Nodes.get_Item("VisitAsia").EnterFinding("visit");

bel=TB.GetBelief("present");

Console.WriteLine("GivenabnormalX-RayandvisittoAsia,theprobabilityofTBis"+

bel.ToString("G4"));

net.Nodes.get_Item("Cancer").EnterFinding("present");

bel=TB.GetBelief("present");

Console.WriteLine("GivenabnormalX-Ray,Asiavisit,andlungcancer,theprobabilityofTBis

"+bel.ToString("G4"));

net.Delete();

if(!app.UserControl)app.Quit();

Console.WriteLine("Press<enter>toquit.");

Console.ReadLine();

}

}

}

VisualBasicExampleCodeBelowisanexampleVBprogramthatdoesthesamethingasthe"Demo"programthatshipswithNeticaC-API.ThereisaVisualStudioprojectforit,called"NeticaDemoforVB"withinthe"Netica\Neticaxxx\ProgrammingExamples"folderoftheNeticadownloadpackage.(moreinfoonprogrammingNeticainVB)

SubMain()OnErrorGoToFailed

DimappAsNetica.Application

app=NewNetica.Application

app.Visible=True

Dimnet_file_nameAsString

net_file_name=System.AppDomain.CurrentDomain.BaseDirectory()&"..\..\..\ChestClinic.dne"

DimnetAsNetica.Bnet

net=app.ReadBNet(app.NewStream(net_file_name))

net.Compile()

DimTBAsNetica.BNode

TB=net.Nodes.Item("Tuberculosis")

DimbeliefAsDouble

belief=TB.GetBelief("present")

MsgBox("Theprobabilityoftuberculosisis"&belief)

net.Nodes.Item("XRay").EnterFinding("abnormal")

belief=TB.GetBelief("present")

MsgBox("GivenanabnormalX-Ray,theprobabilityoftuberculosisis"&belief)

net.Nodes.Item("VisitAsia").EnterFinding("visit")

belief=TB.GetBelief("present")

MsgBox("GivenabnormalX-RayandvisittoAsia,theprobabilityoftuberculosisis"&belief)

net.Nodes.Item("Cancer").EnterFinding("present")

belief=TB.GetBelief("present")

MsgBox("GivenabnormalX-Ray,Asiavisit,andlungcancer,theprobabilityoftuberculosisis"&belief)

net.Delete()

IfNotapp.UserControlThen

app.Quit()

EndIf

ExitSub

Failed:

MsgBox("NeticaDemo:Error"&(Err.NumberAnd&H7FFFS)&":"&Err.Description)

EndSub

Belowisanexamplethatreadsinanetfromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_examples_folder.htm');returnfalse;">Examplesfolder(youmayhavetochangethepath),thenreadsincasesanddoesbeliefupdating.------------------------------SubMain()OnErrorGoToFailed

DimappAsNetica.Application

app=NewNetica.Application

DimcasefileAsStreamer

DimnetAsBnet

Setnetfile=app.NewStream("C:\NeticaData\BNs\Car_Diagnosis_0_Learned.dne")

Setcasefile=app.NewStream("C:\NeticaData\Cases\GoodCases\CarCases10.cas")

Setnet=app.ReadBNet(netfile)

net.AutoUpdate=1

net.Compile

Dimlights_nodeAsBnode

Setlights_node=net.Node("Lights")

Dimlights_dimAsLong

lights_dim=lights_node.GetStateIndex("dim")

DimidAsLong

DimfrAsDouble

DimcaseposnAsLong

DimdoneAsBoolean

done=False

caseposn=FirstCase

Do

net.RetractFindings

net.ReadFindingscase_posn:=caseposn,stream:=casefile,IDNum:=id,freq:=fr

net.ReadFindingscase_posn:=caseposn,stream:=casefile,nodes:=net.Nodes,IDNum:=id,freq:=fr

Ifcaseposn=NoMoreCasesThen

done=True

Else

MsgBox"BeliefinLightsdim="&lights_node.GetBelief(lights_dim)

EndIf

caseposn=NextCase

LoopUntildone

net.Delete

ExitSub

Failed:

MsgBox"Error"&((err.NumberAnd&H7FFF)-10000)&":"&err.Description

EndSub

===============================================================================EXAMPLESONHOWTOSETCPTTABLEENTRIES:-----------------------------------------HereishowyoucouldsettheCPTsofthe"ChestClinic"examplefromthemanual:

DimVisitAsiaAsBNode,TuberculosisAsBNode,SmokingAsBNode

DimCancerAsBNode,XRayAsBNode,TbOrCaAsBNode

SetVisitAsia=net.Node("VisitAsia")

...

SetTbOrCa=net.Node("TbOrCa")

Dimp(0To1)AsSingle

p(0)=0.01:p(1)=0.99:VisitAsia.CPTable("")=p

p(0)=0.05:p(1)=0.95:Tuberculosis.CPTable(Array(0))=p

p(0)=0.01:p(1)=0.99:Tuberculosis.CPTable(Array(1))=p

p(0)=0.5:p(1)=0.5:Smoking.CPTable("")=p

p(0)=0.1:p(1)=0.9:Cancer.CPTable(Array(0))=p:

p(0)=0.01:p(1)=0.99:Cancer.CPTable(Array(1))=p

p(0)=0.98:p(1)=0.02:XRay.CPTable(Array(0))=p

p(0)=0.05:p(1)=0.95:XRay.CPTable(Array(1))=p

p(0)=1:p(1)=0:TbOrCa.CPTable(Array(0,0))=p:

p(0)=1:p(1)=0:TbOrCa.CPTable(Array(0,1))=p:

p(0)=1:p(1)=0:TbOrCa.CPTable(Array(1,0))=p:

p(0)=0:p(1)=1:TbOrCa.CPTable(Array(1,1))=p:

Hereare6alternatewaystosettheCPToftheTbOrCanode.Dimp(0To1)AsSingle

Dims(0To1)AsInteger

s(1)=0:s(0)=0:p(0)=1:p(1)=0:TbOrCa.CPTable(s)=p:

s(0)=1:TbOrCa.CPTable(s)=p:

s(1)=1:s(0)=0:TbOrCa.CPTable(s)=p:

s(0)=1:p(0)=0:p(1)=1:TbOrCa.CPTable(s)=p:

Dimp(0To1)AsSingle

p(0)=1:p(1)=0:TbOrCa.CPTable("present,present")=p:

p(0)=1:p(1)=0:TbOrCa.CPTable("present,absent")=p:

p(0)=1:p(1)=0:TbOrCa.CPTable("absent,present")=p:

p(0)=0:p(1)=1:TbOrCa.CPTable("absent,absent")=p:

TbOrCa.StateFuncTable("present,present")="true":

TbOrCa.StateFuncTable("present,absent")="true":

TbOrCa.StateFuncTable("absent,present")="true":

TbOrCa.StateFuncTable("absent,absent")="false":

TbOrCa.CPTable("*,*")=Array(1,0)

TbOrCa.CPTable("absent,absent")=Array(0,1)

TbOrCa.StateFuncTable("*,*")="true"

TbOrCa.StateFuncTable("absent,absent")="false"

TbOrCa.Equation="TbOrCa(Tuberculosis,Cancer)=(Tuberculosis||Cancer)"

TbOrCa.EquationToTablenum_samples:=1,samp_unc:=False,add_exist:=False

ManagedC++ExampleCodeBelowisanexampleManagedC++(i.e.,"C++/CLI")programthatdoesthesamethingasthe"Demo"programthatshipswithNeticaC-API.ThereisaVisualStudioprojectforit,called"NeticaDemoforCLRC++"withinthe"Netica\Neticaxxx\ProgrammingExamples"folderoftheNeticadownloadpackage.(moreinfoonprogrammingNeticainManagedC++)

usingnamespaceSystem;usingnamespaceNetica;intmain(array<String^>^args){

Console::WriteLine("WelcometoNeticaAPIforManagedC++!");

Netica::Application^app=gcnewNetica::Application;

app->Visible=true;

String^net_file_name=AppDomain::CurrentDomain->BaseDirectory+"..\\ChestClinic.dne";

Streamer^file=app->NewStream(net_file_name,nullptr);

BNet^net=app->ReadBNet(file,"");

net->Compile();

BNode^TB=net->Nodes->Item["Tuberculosis"];

doublebel=TB->GetBelief("present");

Console::WriteLine("Theprobabilityoftuberculosisis"+bel);

BNode^XRay=net->Nodes->Item["XRay"];

XRay->EnterFinding("abnormal");

bel=TB->GetBelief("present");

Console::WriteLine("GivenanabnormalX-Ray,theprobabilityoftuberculosisis"+bel);

net->Nodes->Item["Cancer"]->EnterFinding("present");

bel=TB->GetBelief("present");

Console::WriteLine("GivenabnormalX-Ray,Asiavisit,andlungcancer,theprobabilityofTBis"+bel);

net->Delete();

if(!app->UserControl)app->Quit();

Console::WriteLine("Press<enter>toquit.");

Console::ReadLine();

return0;

}

Non-EnglishBayesNetsAlthoughNeticaApplicationisinEnglish,itcanbeusedtobuildBayesnetsinanylanguage.Neticacanworkwithnon-Latinandinternationalcharactersets(suchasChinese,Japanese,Arabic,Hebrew,orUnicode),includinggeneratingSVGgraphicswiththosecharacters.

ThefollowingaretheplaceswhereNeticawillaccepttextinanycharacterset:

•Titleofeachnode(notitsname).•Titlesofallthestatesofeachnode(nottheirnames).•Comment(description)ofeachnode.•Commentsforeachstateofeachnode.•Titleofthenet(notitsname).•Overallcomment(description)ofthenet.•User-definedfieldsofnodesandthenet.

ThesearesufficientfortheBayesnetdevelopertoprovidetheend-userwithaBayesnetintheirnativelanguage.

HowTo:Inanyoftheaboveplaces,youcanpasteintextfromanotherprogramwhichusesacharactersetbasedon=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Unicode.htm');returnfalse;">Unicode.OryoucanchangethecharactersetfromtheWindowstaskbar,andthentypeinthecharacters.Oryoucanuse=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPItoset/getthemwithUnicodestrings.

Font:Makesureyouchoosenodefonts,whicharecapableofdisplayingthecharactersyoudesire.AUnicodecapablefont,suchasArialUnicodeMS,isusuallyasafechoice.

BlackRectangles:Youmayjustseejustblackrectangleswherethereshouldbenon-Englishtext.Iftheyappearonthenetdiagram,theproblemisthatthefontthatyouhavegiventhenodesisnotcapableofdisplayingthecharacters(asdescribedintheparagraphabove).Iftheyappearwithindialogboxes,

yourcomputerneedstobeconfiguredtodisplaythecharacters(asdescribedintheparagraphbelow).Ifthedialogboxcontainsarowofquestionmarksinstead,thatindicatesaninvalidplacetobeenteringnon-Englishtext.

ConfiguringComputer:TomakeinternationalcharactersetsavailablefromtheWindowsXPtaskbar,chooseStart→Settings→ControlPanel→RegionalandLanguageOptions→Languages.Ifyoudesireoneofthelanguagesmentionedatthebottomcheck-boxes,andtheboxisnotcheck-marked,firstcheck-markthebox,clickOK,restartyourcomputer,andreturntothisdialogbox.

ThenclickDetails→Settings→Add,chooseaninputlanguage,keyboardlayoutandclickOK.YoucannowswitchbetweendifferentinputlanguagesusingtheLanguageBar,whichwillappear(usuallyontherightsideoftheWindowstaskbar).

WebsitesforCharacters:Forsomecharactersetsitismoreconvenienttogeneratethecharacterswithaspecialprogramorwebsite.

Forexample,see:http://code.cside.com/Inparticular:http://code.cside.com/3rdpage/utf-8/and

http://people.w3.org/rishida/scripts/pickers/

CommandLineOptionsIfNeticaisrunfromthecommandlineitcanacceptaNeticapassword,whichisusedforthatsession,butnotenteredintotheregistry.

IfNeticaisrunwithcommandlineparameters,thenonstart-up,Neticawillputinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowalineshowingwhatcommandlineparameterswereused.

SetPath:TorunNeticafromthecommandline,youmuststartitfromthedirectorythatcontainstheNeticaApplicationexecutable(i.e.theNetica=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_NeticaHomeFolder.htm');returnfalse;">homedirectory).Alternately,youcanincludethehomedirectorywiththeNeticafilename(suchastypingsomethinglikeC:\ProgramFiles\Netica\Netica317\Netica.exeallenclosedindoublequoteswherenecessary).Athird,morepermanent,choiceistoputtheNeticahomedirectoryintheMSWindowspathenvironmentvariable.

YoucanfindthehomedirectoryfromNeticabychoosingHelp→AboutNetica,andthenlookingintheMessageswindow.

Youcanaddtotheenvironmentpathvariablebyfollowing:

Start→Settings→ControlPanel→System→Advanced→EnvironmentVariables→Path→Edit.

ThenaddasemicolonandtheNetica=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_NeticaHomeFolder.htm');returnfalse;">homedirectorytotheend.

Running:Bringupthecommandlinedialogboxbyfollowing:Start→Run...ThentypeinthefilenameofNetica(e.g.Neticaor"Netica325").Or,youcanusetheshellinterpreter,availablebychoosingStart→Programs→

Accessories→CommandPrompt.

Notethatyouneedthequotesifthereisaspaceinthefilename.Whenyoupressokay,Neticashouldcomeup.

Options:YoucanputcommandlineargumentsaftertheNeticafilenametoachievecertainresults.Thefollowingaretheoptions:

<file-name>WhenNeticastartsup,itwillopentheBayesnetwiththegivenfilename.Youwillneedtoputthefullpath,anddon'tforgetquotesarounditiftherearespacesinthename.IfthenetwascompiledandAutoUpdatingwasturnedonwhenitwaslastsaved,thenwhenitcomesupinNetica,itwillbeallreadytogo.Example:"Netica305""C:\NeticaData\MyBN.neta"

-print<file-name>PrintstheindicatedBayesnetfileonthedefaultprinteringraphicalformat.-case<file-name>Readsthefirstcasefromtheindicatedfile,intotheBayesnetithasopened.ThisoptionmustfollowanoptiontoreadinaBayesnet.Example:Netica"C:\Data\MyBN.neta"/case"C:\Data\MyCase.cas"

-password<pw>RunsNeticawiththegivenlicensepassword.Ignoresanyinstalled=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_CY_password.htm');returnfalse;">password.ItusesthepasswordforthissessionofNeticaonly(i.e.itdoesn'tinstallthepasswordonthecomputerforthenexttimeNeticaisrun).-EmbeddingThisisonlyforthoseusingtheCOMinterface(ithastheusualmeaningunderCOM).

Example:IfthefollowingisrunfromthedirectorycontainingBayesnetfile"ChestClinic.dne"andcasefile"NoAsia.cas"(andthehomedirectoryisonthesystempath):

>NeticaChestClinic.dne-caseNoAsia.cas

ItwillbringupNetica,openthechestclinicnet,andreadtheNoAsiacaseintothatnet.

Underprogramcontrol:YoumaywanttolaunchNeticadirectlyfromanotherprogram.Mostdevelopmentsystemshaveafunctiontosendacommandtotheoperatingsystem(e.g.ashellcommand).

Forexample,ifyouareprogramminginC/C++,youcouldcalltheWin32functionCreateProcess,orthefunctionWinExec,asfollows:

WinExec("Netica.exe",SW_SHOWNORMAL);

Allthecommandlineoptionswork,soyoucouldcall:

WinExec("\"C:\\Netica\\Netica307.exe\"C:\\Data\\MyBN.neta",SW_SHOWNORMAL);

ObfuscatingaNetIftheprotectionofintellectualproperty,orproprietaryorclassifiedinformationisaconcernforyou,NeticahastheabilitytoobfuscateyournetandtoworkwithencryptedBayesnets.Thesemanticcontentofthenetisretained,soinferenceresultswillnotbeaffected.

HowTo:Ifyouaregoingtosendthenettosomeoneelse,butithasproprietaryinformationthatyoudon'twanttorevealtootherusers,chooseModify→Obfuscatenet.Anewwindowwillopenwiththeobfuscatednet.Ifyouselectnodesbeforeyouobfuscate,itwillonlyapplytothosenodes.Ifnonodesareselected,itwillapplytotheentirenet.

Action:Allidentifyinginformationassociatedwiththenet(includingnodename,nodetitle,nodecomment,statename,statetitle,statecomment,nettitle,netcomment,netfilename,linknames,node-setnames)willberemovedorconvertedintonon-identifyinglabels.

XRefReport:Thesechangesareloggedintothe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindowforfuturereference,calledacrossreferencereport.IfyouwishtopastetheseresultsintoanExcelspreadsheet,selectthetextinthecrossreferencereport(excludingthereportheading)andchooseModify→TabifySelection,thenpressCTRL+Ctocopythetable.InanExcelworkbook,pressCTRL+Vtopastethetable.

Youcanusethecrossreferencereportasakeytotranslatebetweenthefullnetandtheobfuscatednet.Forinstance,iftheobfuscatednetistobepartofapackagecontainingsoftwarethatusesNeticaAPItoreadinthenet,entersomefindingsandperformsomequeries,thenthekeywillcontaintheinformationneededtoconvertthefamiliarnamestotheonesneededbyNeticaAPI.

Encryption:AnotherwaytoprotectorhidetheinformationinaBayesnet,istouseNetica'sencryptioncapability.Infact,anetcanbebothobfuscatedandencrypted.

EncryptingaNetNeticaoffersstrong(64bit)encryptionofBayesnets.ItmaybeusedforsecurityduringthedevelopmentofclassifiedBayesnets,ortoprotectyourIPwhendistributingBayesnets.

HowTo:Makethenetthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_active_window.htm');returnfalse;">activewindow,chooseFile→EncryptionPassword,andenterthepasswordyouwishtouse.Fromthenon,eachtimeyousavethenet,itwillbeinencryptedform.

Onceanetissavedinencryptedform,theonlywaytoreaditisusingNetica,andtosupplyNeticawiththesamepasswordusedtoencryptit.

ForNeticaAPI:EncryptionisoftenusedtoprotectIPwhendistributingaBayesnetinapackagewhichalsocontainsNeticaAPIandaspecializedprogramthatisgoingtousethenetviaNeticaAPI.Thespecializedprogramhasthepasswordbuiltintoit(possiblyinmutatedordistributedformtoevadedetection),anditusesthatpasswordwhenitcallsNeticaAPItoreadintheBayesnet.

Obfuscation:WhenyouwanttohidetheidentifyinginformationinaBayesnet,butyoucan'tuseencryptionbecauseyouhavetomakethenetavailable,thenobfuscatingthenetmaybeabetterchoice.

CustomizingtheToolbarTochangeNetica’stoolbar,simplydouble-clickonablankareaofthetoolbar,orchooseWindow→CustomizeToolbar,andusetheresultingdialogboxtomakedesiredchanges.Thedialogboxwilllooksomethinglikethis:

Toaddbuttonstothetoolbar,dragthemfromtheleftlisttotherightlist(orhighlightitandclickAdd).Dothereversetoremovebuttonsfromthetoolbar.Toaddaseparator,dragitfromthetopoftheleftlisttowhereveryouwouldlikeoneontherightlist.Buttonsintherightlistcanalsobedraggedupanddowntocreateanidealorder.Pressingthe"Reset"buttonsetsthetoolbartoNetica'soriginalbuttons.Whenyouaresatisfiedwithyourchanges,clickClosetosavethem.

Oncetheyareonthetoolbar,buttonscanberearrangedorremovedmanuallybyholdingdowntheALTkeywhiledraggingthem.YourchangeswillbesavedwhenyouexitNetica,sothattheyareavailableforthenextsession.

Manyofthesetoolbarbuttonsareassociatedwithacceleratorkeys.Foralistofshortcutkeysandtheirfunctions,clickhere.

GroupingNodeStatesSometimesitisusefultoorganizethestatesofanodeintogroups,whicheffectivelygivesitacoarserresolution.BoththefinerresolutionandthecoarseronecanbeusedinthesameBayesnet.Sincethecoarsernodeislessprecise,usingitinsteadofthefineonewillresultinlesspreciseresults,butthedifferencemightbeinsignificant.

Youhavetojudgewhatisappropriateforyourparticularapplication.

ForExample:Youmaywanttogroupthestatesofacountryintoregions.ForexamplethefinernodewouldhavestatesCA,FL,TX,VA,etc.whilethecoarseonewouldhavestatesWest,Midwest,South,etc.

Anotherexampleisacontinuousnodethatis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizedwithdifferentresolutions.Forexampleacoarsetemperaturenodemayhavethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_threshold.htm');returnfalse;">thresholds0,10,20,etc.whilethefineonehasthresholds0,5,10,15,etc.

Reasonsforgroupingstates:

•Becauseyouhaveprobabilitiesforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTsofothernodesgiventhecoarsenode,butnotgiventhefinenode.Orperhapsyoujustwanttoelicittheprobabilitiesrelatingtothecoarsenodebecausethetablesaresmaller,anditiseasier.

•YouwanttheBayesnettolearnfrommultipledatasources(e.g.twodifferentdatabases),andtheydescribevariablesindifferentways(perhapsoneismoredetailed,andprovidesmorepossiblestatesforavariable).

•Toeasethecomputationalburden(e.g.usingthecoarsenodeinsteadofthefineoneastheparenttothosenodesthathavealotofotherparents).

•Youwanttodisplayresultsinsummarizedform.Perhapstheend-userviewingthebelief-bardisplaywantstoseetheprobabilitiesforawholegroupofstates,insteadofadetailedbreakdown.

•Youmaywanttoallowfortheentryoffindingsthataren'tspecifiedprecisely.Forexample,allowinganentryof"car"foraVehicle_Typenode,ratherthan"sedan","stationwagon",etc.sincethatinformationmightnotbeknown.Essentially,thisresultsinenteringalogicaldisjunctionoverthefinerstates.

•Youareonlyinterestedinoneparticularstate,andyougrouptherestofthemtogetheras"other".

HowTo:Maketwonodesandgivethemnamesthatarealmostthesame,toindicatetheyareforthesamevariable.Perhapsthecoarseronecouldbesuffixedwith"_Approx".Sometimesitisbesttoappendawordwhichdescribesthelevelofresolution,suchas"Country","Region"or"Province".

Onenodeshouldbegiventhesetoffinestates,theothergiventhesetofcoarsestates.

Inthecaseofacontinuousvariable,thefinernodewouldhavethesamethresholdlevelsasthecoarseone,butwithsomeextrathresholdsadded.Ifthefinenodeismissingsomeofthethresholdsthecoarseonehas,themethodwillstillwork,butwillintroduceextrauncertainty,sinceNeticamustturnthecoarsenodeintoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_chance_node.htm');returnfalse;">chancenodewhenitbuildsthetable.

Drawalinkfromthefinenodetothecoarsenode.Thatmustbetheonlylinkenteringthecoarsenode(ifyouneedtohaveotherlinksenteringit,usethe"equalityconstraintlink"methodinstead).

Enteratabletoshowthefunctionalrelationshipbetweenthefineandcoarsenodes.Bringupthetableeditorforthecoarsenode,changeitfromChancetoDeterministic,andthengothroughalltherows(theycorrespondtothestatesofthefinenode),enteringintherighthandcolumntheequivalentstateforthecoarsenode(byclickingonitandchoosingfromthemenu).

Insteadyoumaywanttoshowthefunctionalrelationshipwithanequation.

Bringupthenodepropertiesboxforthecoarsenode,usethemulti-purposeselectoratthebottomtochooseEquation,andthenenteranequationlike:

VoterRegion(VoterState)=

(VoterState==CA)?West:

(VoterState==OR)?West:

(VoterState==FL)?South:

...

(VoterState==VA)?East:Other

oryoucouldusethestyle:

VoterRegion(VoterState)=

(VoterState==CA||VoterState==OR||VoterState==WA)?West:

(VoterState==FL||VoterState==TX)?South:

...

(VoterState==VA||VoterState==NY||VoterState==MA)?East:Other

Fordiscretizedcontinuousnodes,yousimpleputanequality,suchas:

Temperature_Approx(Temperature)=Temperature

Afterenteringtheequation,clickOKonthedialog,andconverttheequationtoatable.

Thenlinkthetwonodesintothenetworkthewayyouwant.Eachcanbeaparentorchildtoanyothernodeyouwant,exceptthecoarsenodecannotbeachild.Ifthatisrequired,usean"equalityconstraintlink".

Remember,ifyouareusingNeticatolearnfromdata,givinganodethestate"other"willcatchanystateyouhaven'texplicitlygiventhenode.

CombiningNetsThepurposeofthisfeatureistocombinetheknowledgeoftwoormoreBayesnetsintoasinglenet.Thenetsmayhavebeenlearnedfromdata,orcreatedbyexperts.

Youstartwithonenet(theoriginalnet),andthenaddonanother(theadditionalnet),toformtheresultantnet.Thisprocessmayberepeatedtocombineanynumberofnets.

Ifnodesineachofthenetshavethesamename(regardlessofstates),theywillbeinterpretedasstandingforthesamevariable,andwillresultinasinglenodeintheresultantnet.Amongnodeshavingthesamename,theresultantnodewillhaveallthestatesoftheoriginalnodeandthestatesoftheadditionalnode.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTswillbecombinedaccordingly.

Howto:Openyouroriginalnet,orcreateanewone.ChooseModify→CombineNets,andfromthestandardfile-opendialogbox,picktheBayesnetfiletobeaddedon.Ifyouwishtocombineseveralnets,thenafteraddingthefirstone,successivelyaddtheothersinthesameway.

Neticawillnextaskyoutoenteradegreefortheadditionalnet.Itisanamounttoweighttheknowledgeinthatnetrelativetothefirstnet.Youwillalmostalwaysacceptthedefaultof1.0,sincetheexperienceamountsalreadyweightthenetsrelativetoeachother,andthedegreeisjustanextra"experiencemultiplier"toprovideaddedflexibility(seebelow).

Experience:Ifthenetswerelearnedfromdata,thentheywillhave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_experience.htm');returnfalse;">experiencetablesaswellas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTtables,whichwillweightthenetsaccordingtohowmuchdatawasusedtolearneachone.Ifthenetswerecreatedbyexpertsratherthanlearnedfromdata,theymay

haveCPTtableswithnoexperiencetables.Inthatcaseyouwillbepromptedforasingleexperiencenumbertobeappliedtothewholenet.Theeffectofthenumberyouenterisjusttoweightthenetsproducedbyeachexpert,buttheideaistoenteranumberthatisanestimateoftheequivalentnumberofcasesseenbythatexpert.Ifyouwishtohavemorecontrolovertheexperienceamounts(forinstance,differentnumbersforeachnode,orevenatableofdifferentnumbersforeachnode),thenentertheexperiencetablesbeforedoingthecombiningoperation.

Structure:Thestructureoftheoriginalnetandtheadditionalnetdonothavetobethesame,buttheymustbecompatible.Ifindoubt,trycombiningthemandobservingtheresultsobtained.Youmaywanttoadjustthestructureofoneorbothnetsbefore-handtomakethemcompatible.Forthatpurposeyoucanuselinkreversals,orevenbetter,youcanconstructtheCPTableswithBuildFromOtherNet.

Degree:ThewaythatNeticausesthedegreeasanexperiencemultiplieris:Ifthedegreeislessthanoneitmultipliesallexperiencenumbersoftheadditionalnetbythedegree,andifitismorethanone,itmultipliesalltheexperiencenumbersoftheoriginalnetby1/degree.Soexperiencenumbersareneverincreased,andthemagnitudeofthedegreeindicateshowmuchmorereliabletheadditionalnetiscomparedtotheoriginalnet.

Alternative:Anotherwaytocombinenetsistocopynodesfromtheadditionalnet,andthenpastethemintotheoriginalnet.Youmighthavetohookupsomedisconnectedlinks.ThatmethodwillnotcombineCPTtables.

ShortcutKeysforNetica

F1 HelpINFO

F3 FindNextINFO

SHIFT F4 TileWindowsINFO

CTRL F4 CloseWindowINFO

ALT F4 ExitNeticaINFO

SHIFT F5 CascadeWindowsINFO

F6 RandomCaseINFO

F7 PasteINFO

F8 GetNextCaseINFO

SHIFT F8 GetPreviousCaseINFO

F9 AddNode(single)INFO

F9-F9 AddNode(multiple)INFO

F10 AddLink,(single)INFO

F10-F10 AddLink(multiple)INFO

CTRL A SelectAllINFO

CTRL+SHIFT A InvertSelectionINFO

CTRL B ReportBeliefsINFO

CTRL C CopyINFO

CTRL E ReportCase(Evidence)INFO

CTRL F FindINFO

CTRL G MakeSVGGraphicINFO

CTRL+SHIFT G GoBackINFO

CTRL L LearnFromCaseINFO

CTRL N NewBayesNetWindowINFO

CTRL+SHIFT N NewNode-SetINFO

CTRL O OpenFileINFO

CTRL P PrintINFO

CTRL R RemoveFindingsINFO

CTRL S SaveINFO

CTRL+SHIFT S SelectNode-SetINFO

CTRL T EditTable(CPT)INFO

CTRL U UpdatebySamplingINFO

CTRL V PasteINFO

CTRL W CloseWindowINFO

x Fillwithimpossiblecharacter,CPTTable

INFO

CTRL X CutINFO

CTRL Y RedoINFO

CTRL+SHIFT Z RedoINFO

CTRL Z UndoINFO

0 Fillwith0,CPTTableINFO

CTRL 0 FillinMissingCPTEntriesINFO

CTRL 1 NormalizeCPTRoworTableINFO

CTRL 8 SelectIncompleteCPTTableINFO

CTRL SelectIncompleteCPTTableINFO

= MakeuniformCTPTableINFO

CTRL Insert CopyINFO

SHIFT Insert PasteINFO

CTRL Tab CyclesAmongOpenWindows

ALT Tab CyclesThroughRunningApplications

ALT Enter DisplaysPropertiesofSelectedItem

CTRL > ZoomOutINFO

CTRL < ZoomInINFO

CTRL+SHIFT > ZoomToFitINFO

CTRL+SHIFT < ZoomToNormalINFO

CTRL+ALT > ZoomToPercentageINFO

CTRL+ALT < ZoomBackINFO

SpaceBar ZoomGlobalINFO

ALT Back UndoINFO

SHIFT Delete CutINFO

Delete DeleteINFO

Pause NormalModeINFO

GeneralMSWindowsshortcuts:ALT+UNDERLINEDLETTERSinthemenudoesthecorrespondingmenucommandWINDOW+LlockscomputerCTRL+DRAGduplicateswhatisbeingdragged

Youmaywanttoprintouttheabovetable,tokeepasahandyreferenceguide.

FileFormatsBayesNetFiles.dne R/W NeticaBayesnetfileintextformINFO

.neta R/W NeticaBayesnetfileinbinaryform(possiblyencrypted)INFO

.net R HugintextfileforBayesnets.NeticacanreadfilescreatedbyHugin4.*,5.*and6.*INFO

.dxp R KnowledgeIndustriesfileforDXpress

.dsc R BNIFfile

.ergo R NoeticSystemsfileforErgoINFO

CaseFilesorDataFiles.cas R/W NeticacasefileINFO

.uvf R/W NeticacasefileinUVF(uncertainvalueformat)INFO

.csv R/W Commaseparatedvalue(mayhaveotherextensions)INFO

.txt R/W Tabdelimitedtext(mayhaveotherextensions)INFO

GraphicsFiles.svg W XMLscalablevectorgraphicsfileINFO

.svgz W CompressedSVGfileINFO

TextFiles.txt R/W Asciitextfile(mayhaveotherextensions)INFO

.dne R/W INFO

.cas R/W INFO

.xml R INFO

.svg W INFO

"R"meansNeticacanreadthefileand"W"meansitcanwritethefile.

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Clemen,RobertandTerenceReilly(2001)MakingHardDecisionswithDecisionTools,Brooks/Cole,PacificGrove,CA.

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Darwiche,Adnan(2009)ModelingandReasoningwithBayesianNetworks,CambridgeUniversityPress.

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Smith,JamesE.,SamuelHoltzmanandJamesE.Matheson(1993)“Structuringconditionalrelationshipsininfluencediagrams”inOperationsResearch,41(2),280-297.

Spiegelhalter,DavidJ.,A.PhilipDawid,SteffenL.LauritzenandRobertG.Cowell(1993)“Bayesiananalysisinexpertsystems”inStatisticalScience,8(3),219-283.

Spirtes,Peter,ClarkGlymourandRichardScheines(2000)Causation,Prediction,andSearchSecondEdition,TheMITPress,Cambridge,MA.

Zhang,Lianwen(Nevin),RunpingQiandDavidPoole(1994)“Acomputationaltheoryofdecisionnetworks”inInternationalJournalofApproximateReasoning,11(2),83-158.

GlossaryA-EAbsorption:NodeabsorptionistheprocessofremovinganodefromaBayesnetordecisionnet,andadjustingtheremaininglinksandnodetablessothatsubsequentinferencedoneontheremainingnodeswillyieldthesameresults.UsuallyNeticahastoaddsomenewlinkstomaintaintheglobalrelationshipsbetweenthenodes.MoreInfo

ActiveWindow:Menuandkeycommandsgenerallyapplytotheactivewindow,whichisthewindowwiththenon-dimtitlebar,andisthefrontmostwindow(exceptpossiblyforsomedialogboxesandhelpwindows).Youcanmakeawindowactivebyclickingonanexposedpartofit,orbychoosingitstitlefromtheWindowmenu.

ASCII:ASCIIisatextcharacterencodingbasedontheEnglishalphabet,andwasfirstreleasedasastandardin1967.Itrepresentseachcharacterwith7bits,althoughtherearemany8-bitextensionsofit.ASCIIanditsextensionshavebeenbyfarthedominantwaytorepresenttextinacomputer,butarenowbeingovertakenby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Unicode.htm');returnfalse;">Unicode,whichcanrepresentmanymorecharacters.InNetica,identifiers(i.e.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_IDname.htm');returnfalse;">IDnames)arealwayscomposedonlyofASCIIcharacters,whiletitlesanddescriptionsmaybeinUnicode.

Assessment:Probabilityassessmentistheprocessofhumansdeterminingtheprobabilisticordeterministicrelationshipsbetweennodesandtheirparents(usuallyintheformof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobabilitytables)afterallthenodesandthelinkstructurehavebeencreated.Alternatively,theycanbedeterminedautomaticallybysomelearningprocedure.

Auto-updating:IfaBayesnetisauto-updating,thenwheneverits=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsbecomeinvalid,perhapsdueto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteringnewfindings,theyareautomatically=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">recalculated(providedthenetis=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compiled).Sinceupdatingmaybetimeconsuming,youmayprefertoonlyhavethenetupdatedwhenyoumanuallyrequestit.Thedefaultfornewnetsisthattheyareauto-updating.MoreInfo

Background:ThebackgroundofaBayesnetordecisionnetisthearea(withinitswindow)whichisnotcoveredbyanodeoralink.

Barrennode:Abarrennodeisanodewithno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">children,andthatisnota=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_findings_node.htm');returnfalse;">findingsnodeora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_query_node.htm');returnfalse;">targetnode.During=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingandfinding=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_optimal_policy.htm');returnfalse;">optimaldecisions,nodesthatarebarrendon’tinfluencetheresults,andmaysimplyberemoved.

Bayesnet:ABayesnet(alsoknownasabeliefnet)iscomposedofasetofnodesrepresentingvariablesofinterest,connectedbylinkstoindicatedependencies,andcontaininginformationabouttherelationshipsbetweenthenodes(oftenintheformofconditionalprobabilities).Usagesincludeprediction,diagnosis,probabilisticmodeling,learningfromdataandformingabasisforbuilding=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.MoreInfo

Belief:Thebeliefofanodeisthesetofprobabilities(oneforeachofitspossiblestates),takingintoaccountthecurrentlyenteredfindingsbyusingtheknowledgeencodedintheBayesnet.Technicallyspeaking,itisthemarginalposteriorprobabilitydistributionofthenode,giventhefindingsandtheBayesnetmodel.Sometimesthepluralform“beliefs”isusedtomeaneachoftheprobabilitiesintheset.

Beliefupdating:Beliefupdatingistheprocessoffindingnew=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsforthenodesofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnettoaccountforthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsthatarecurrentlyknown.Itisaformofprobabilisticinference.DuringbeliefupdatingtheBayesnetmodel(inparticular,the=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobabilitytablesbetweenthenodes)isnotmodifiedatall;forthat=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probability_revision.htm');returnfalse;">probabilityrevisionisused.MoreInfo

Bernoulliprocess:ABernoulliprocessconsistsofaseriesofindependent

trials,eachwithtwopossibleoutcomes(oftenlabeled"success"and"failure"),withaconstantprobability,p,ofsuccess(suchasasetofcointosses).Iftherearentrials,itisalsocalledabinomialexperiment,andthetotalnumberofsuccesses,k,isgivenbythebinomialdistribution.Thenumberoftrialsneededbeforegettingafixednumberofsuccessesisgivenbyanegativebinomialdistribution,andthenumberoftrialsneededtogetonesuccessisgivenbyageometricdistribution.Iftherearemorethantwopossibleoutcomes,itisamultinomialexperiment,anditsresultsaregivenbyamultinomialdistribution.

Binarynode:Abinarynodeisanodewithexactlytwo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">states.Ifthosestatescorrespondto‘true’and‘false’,thenitisalsocalleda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleannode.

Binomialcoefficient:Thebinomialcoefficient,denotedbinomial(n,k),isthenumberofdifferentk-sizedgroupsthatcanbedrawnfromasetofndistinctelements.Itsvalueisgivenby:binomial(n,k)=n!/(k!*(n-k)!)WithinaNeticaequation,youcanrepresentitwiththebinomialfunction.

Booleannode:Abooleannodeisanodewithtwostates,andwhosestatenamesare(true,false),(yes,no),(present,absent)or(on,off).Thesestatenamescanbeineitherorder,andinloweroruppercase(suchasTrueorTRUE).Somepeoplerefertothemas“propositionalnodes”.Theyareexamplesof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_binary_node.htm');returnfalse;">binarynodes.

Cartesianproduct:Thecartesianproductoftwosetsisthesetofallpossiblepairsofelements,wherethefirstelementofeachpairistakenfromthefirstset,andthesecondelementistakenfromthesecondset.Forexample,thecartesianproductof{low,medium,high}with{true,false}is{(low,true),(low,false),(medium,true),(medium,false),(high,true),(high,false)}MoreInfo

Case:Acaseisasetof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingsthatgotogethertoprovideinformationononeobject,event,history,person,orotherthing.MoreInfo

Casesymbol:Thecasesymbolisatinyyellowpagewithwritingtodepictalistofattributesandvalues.Itlookslikethis: Itisusedontoolbarbuttonstoindicatea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">case.

Forexample,the buttonremovesthecurrentcase,the buttonsavesthecasetoafile,andthe buttonreadsacasefromfile.

Centrallimittheorem:Thecentrallimittheoremstatesthatthedistributionofthesumofasetofrandomvariablesapproachesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_normal_distribution.htm');returnfalse;">normaldistributionasthenumberofvariablesincreases,providedtheyareindependentandsomeotherweakconditions(suchasLiapounov'sconditions)aremet.Theseconditionswillalwaysbemetiftheyareidenticallydistributedandtheirmeansandstandarddeviationsexist.

Chancenode:Achancenodeisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenodewhose=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationshipwithits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsisprobabilistic(i.e.notdeterministic).Ifitsparentsvaluesareallknown,andthereisnofurtherinformation,thenitsvaluecanonlybeinferredasaprobabilitydistributionoverpossiblevalues.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicnode.

ChangedIndicator:Achanged-indicator(sometimesknownasa"dirtyindicator")isa*or+afterthetitleofthenetinthenetwindow'stitlebar,andmeansthatthenetcurrentlydisplayedhasbeenchangedfromtheversionsavedtofile.*meansameaningful(i.e."semantic")change,while+meansjustachangetothevisualdisplay.Enteringfindingswillnottriggerthechanged-indicator,unlesstheyareforaconstantnode.Thechanged-indicatorproperlyrespondstoundoandredo.(moreinfo)

A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogcanalsohavea*changed-indicator.Oritcanhavea(*)indicator,whichmeansthatsomethingelsehaschangedthetarget,whichmakesitdifferentfromtheversioninthedialogbox.MoreInfo

Childnode:Ifthereisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">linkgoingfrom=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodeAtonodeB,thenBissaidtobeachildnodeofA.Somepeoplerefertoitasadirectsuccessor.

Clipboard:Wheneveryoudoacopyoperation(forexamplebychoosingEdit→Copy,orpressingCTRL+C),thematerialyoucopygoestotheclipboard,fromwhichyoucanpasteitwhereyoulike.

Clique:Acliqueisasetofnodesinwhicheachnodeisconnectedtoalltheothernodesoftheset,andthereisn’tanyothernodeinthenetwhichisconnectedtoallthenodesintheset.Somepeoplecallthisa“maximalclique”.WhenNeticacompilesaBayesnet,onestepistofindthecliquesofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_triangulated.htm');returnfalse;">triangulated=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_Markov_network.htm');returnfalse;">Markovnetwork.

Compile:WhenNeticacompilesaBayesnetittakesarepresentationofthenetsimilartowhatyouseeonthescreen,andfromitbuildsanewrepresentationcalleda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontree,whichitcanusetodofast=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">probabilisticinference.MoreInfo

Conditionalprobability:Theconditionalprobabilityofaneventistheprobabilityoftheeventoccurringundercertaingivenconditions.MoreInfo

Conditionallyindependent:AvariableXissaidtobeconditionallyindependentofanothervariableYgivenknowledgeZ,ifobtainingknowledgeaboutthevalueofXdoesnotchangeyourbeliefsaboutthevalueofYwhenyoualreadyknowZ.

Conjugatedistributions:Conjugatedistributionsareprobabilitydistributionsfromafamilyofdistributions,suchthatifthepriordistributionbelongstothefamily,thenforanysamplesizeandanyobservations,theposteriordistributionalsobelongstothefamily.Usuallyeachdistributioninthefamilycanbespecifiedbyoneortwoparameters,soonlytheseparametersneedtobekepttrackofduringprobabilisticinference,whichisparticularlyconvenient.

Constantnode:Sometimesitisusefultohavesomethingthatnormallyactsasafixedconstant,butwhichyoucanchangefromtimetotime.Thatisthepurposeofaconstantnode.MoreInfo

Contingencytable:Acontingencytableprovidesavalue(orsetofvalues)foreachpossibleconfigurationofvaluesforsomegivenvariables.Inotherwords,itspecifiesafunctionofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_cartesian_product.htm',400,145);returnfalse;">cartesianproductofthevariables.Netica’s=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogboxcanbeusedtovieworeditcontingencytables.

Continuousvariable:Acontinuousvariableisonewhichcantakeonavaluebetweenanyothertwovalues,suchas:indoortemperature,timespentwaiting,waterconsumed,colorwavelength,anddirectionoftravel.A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariablecorrespondstoadigitalquantity,whileacontinuousvariablecorrespondstoananalogquantity.MoreInfo

CPT:CPTisanabbreviationforconditionalprobabilitytable(alsoknownas“linkmatrix”),whichisthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_contingency_table.htm');returnfalse;">contingencytableof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobabilitiesstoredateachnode,containingtheprobabilitiesofthenodegiveneachconfigurationof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentvalues.SometimesCPTisusedtorefertothedeterministic=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontableofanode,sincethenode'sconditionalprobabilitiescaneasilybefoundfromthat.Itisaformofnode=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relation,soyouusethetabledialogboxtochangeorviewit.

CSVfile:CSVfileisacommonlyusedtermforaformofcasefileinwhichthenamesofthevariablesappearonthefirstline,andthenbelowareallthecases(i.e.records),witheachcaseonasinglelineandhavingavalueforeach

ofthevariables,andwithallthevaluesandvariablesin=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_file.htm');returnfalse;">textformandseparatedbycommas(i.e."CommaSeparatedValues").Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_tab_delimited_file.htm');returnfalse;">tabdelimitedtext.

Cutset:AcutsetfortwosetsofnodesAandBisathirdsetC,suchthatifallthenodesinCareremovedfromthenet(alongwithalllinksinvolvingthem),thenthereisnopathfromanodeinAtoanodeinB.Seealsoloopcutset.

d-separation:Thed-separationruleenablesyoutoquicklydeterminewhethera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingatonenodecanpossiblychangethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsatanothernodebyonlyconsideringthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructureofaBayesnet.MoreInfo

Dag:Adagisanetwithno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_cycle.htm');returnfalse;">directedcycles(althoughitmayhave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_loop.htm');returnfalse;">undirectedloops).Thewordisashortenedformof“directedacyclicgraph”.

Decisionnet:If=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodes(representingvariablesthatcanbecontrolled)and=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynodes(representingvariablestobeoptimized)areaddedtoa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnet,thenadecisionnet(alsoknownasan“influencediagram”)isformed.MoreInfo

Decisionnode:Adecisionnodeisanodeina=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetwhichrepresentsavariable(orchoice)underthecontrolofthedecisionmaker.Whenthenetissolved,a=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_rule.htm');returnfalse;">decisionruleisfoundforthenodewhichoptimizesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedutility.Decisionnodesarenormallydrawnasrectangles(withoutroundedcorners).

Decisionrule:Adecisionruleindicateswhichoptiontochooseinmakingacertaindecision,foreachpossibleconditionthatmaybeknownwhenthedecisionistobemade.Inotherwords,fora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnode,itisafunctionwhichprovidesavalueforeachmemberofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_cartesian_product.htm');returnfalse;">cartesianproductoftheparentsofthedecisionnode.

Decisiontheory:Decisiontheoryisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_normative.htm');returnfalse;">normative

theorywhichindicateshowasingleagentshouldbestmakedecisionstomaximizehisexpectedutility.Itconsiderssequencesofdecisions,whatinformationtheagentwillhavewhenhemakesthedecisions,uncertaintiesinthebeliefsoftheagent,andcomplexprobabilisticinteractionsintheenvironmentinwhichtheagentisoperating.

Defaultnodestyle:Thereisonedefaultnodestyleforthewholenet,whichisthestyletodisplayanynodewhichdoesn’thaveanoverridingstyle.ItissetbychoosingitfromtheStylemenuwhennonodesareselected.MoreInfo

Deselect:Todeselectallthenodesofanet,clickonitsbackground(i.e.withinthewindow,butnotonanodeorlink).MoreInfo

Deterministicnode:Adeterministicnodeisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenodewhoserelationshipwithits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsisgivenasafunctionoftheparentvalues(i.e.deterministicratherthanprobabilistic).Iftheparentvaluesareallknown,itsvaluecanbedeterminedwithcertainty.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_chance_node.htm');returnfalse;">chancenode.

Deterministicupdating:Beforedoing=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating,Neticadoesdeterministicupdatingwhenitcan,forgreaterspeedandaccuracy.Ifalltheparentsofanodehave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings,andthenodehasa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontableoradeterministicequation,thenitsvaluecanbefoundexactly(the

equationisusedwithout=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretization)veryquickly.

Directedcycle:Adirectedcycle(sometimesjustcalleda“cycle”)isa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_path.htm');returnfalse;">paththroughanet,followingthedirectionofthearrows,whichreturnstoitsbeginning(i.e.thefirstnodeofthepathisthesameasthelast).Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_loop.htm');returnfalse;">undirectedloop.

Neticacanfindanddisplaydirectedcycles.

Directednetwork:Adirectednetworkisonewherethelinkshavedirection(i.e.arrows).Bayesnetsanddecisionnetsareexamples.Comparewithan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_network.htm');returnfalse;">undirectednetwork.

Directedpath:Adirectedpathisasequenceofnodesfroma=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_net.htm');returnfalse;">net,suchthatyoucangetfromonenodeofthesequencetothenextnodebytraversingalinkbetweentheminthedirectionofitsarrow.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_path.htm');returnfalse;">path.

Dirtyindicator:seechangedindicator.

Disconnectedlink:Adisconnectedlinkisonethathasbeendisconnectedfromtheparentnodeitoriginallycamefrom,and=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingcannotproceeduntilthelinkisreconnectedtoitsparent,ortoanothersimilarnode.MoreInfo

Discretenode:Adiscretenodeisanoderepresentinga=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariable.Thestatesofanodeconstitutethedomainofthecategoricalvariable.

Discretevariable:Adiscretevariableisonewithawelldefinedfinitesetofpossiblevalues,called=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">states.Examplesare:thenumberofdimesinapurse,the‘true’or‘false’valueofastatement,whichpartywillwintheelection,thecountryoforigin,andtheplacearoulettewheelstops.Adiscretevariablecorrespondstoadigitalquantity,whilea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousvariablecorrespondstoananalogquantity.MoreInfo

Discretize:Oftenitisusefultohavea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">continuousvariablebehavelikea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discreteone.Todothis,selectthenode(s)andchooseModify→DiscretizeNode.Youcanbreakupthetotalrangeofthecontinuousvariableintoanumberofintervalsbysupplyingnumbersshowingwhereoneintervalendsandthenextbegins(called=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_threshold.htm');returnfalse;">thresholds).Thisisknownasdiscretizingthevariable.Eachintervalresultsinonestateofthediscreteversionofthevariable.MoreInfo

Eliminationorder:Theeliminationorderissimplyanorderedlistofallthenodesinthenet,whichspecifieshowto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_triangulated.htm');returnfalse;">triangulatethenetduring=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compiling(seeSpiegelhalter&DLC93).Triangulationisthemostcriticalstepinproducinganefficientcompilation,sotheorderisincludedwhenthenetisnextsavedtofileifan“OptimizedCompile”command(whichfindsaverygoodeliminationorder)hasbeendone.Theeliminationorderisindicatedbythenumbersfollowingthenodenameswhenyouviewthenetin“triangulatedstyle”.

Ellipsis:Anellipsisisthreecloselyspaceddots,usedtoindicatethatthereismoretofollow,butthatithasbeenleftouttosavespace.Forexample:LongNameFor…

E-mail:The=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">NorsysteamverymuchwelcomesquestionsandcommentsaboutNeticaorthisonscreenhelpdocument.Allinquiresshouldbesentto:support@norsys.com.TodothisdirectlyfromNetica,chooseHelp→EmailNorsys.

Enteringfindings:WhenaBayesnetisappliedtoaparticularsituation,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">case,thentheknowninformationaboutthatcaseisenteredintotheBayesnetbyassigningvalues(called"=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings",or"evidence")totheknownvariables(i.e.nodes),andthatprocessisknownasenteringfindingsintothenodes.Enteringafindingintoaparticularnodedoesnot=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_retract_finding.htm');returnfalse;">retractexistingfindingsatthatnodeorothernodes(butforconvenience,inNetica

Application,ifthenewfindingforanodeflat-outcontradictsapreviouslyenteredfindingforthatnode,thepreviousfindingwillberetractedfirst).MoreInfo

Equation:WithinNetica,theprobabilisticordeterministicrelationshipbetweennodesmaybeexpressedusinganequation,asanalternativeto=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontables.Theequationfollowsasyntaxcommoninmathematicsandcomputerprogramming,andmayuseanyofalargesetofspecialfunctionsbuilt-intoNetica.MoreInfo

Ergo:AprogramavailablefromNoeticSystemsIncorporatedwhichworkswithBayesnets.IfyouhaveBayesnetfilesintheoldErgoformat(i.e.not.entfiles)whichyouwishtousewithNetica,thengivethemafileextensionof".ergo"andNeticawillbeabletoreadthem.

Errorrate:Ifaclassifieristestedonanumberofcases,eachofknownclass,onecandeterminehowmanytimesitmisclassifiedacase(i.e.saidthecasebelongedtosomeclasswheninfactitbelongedtoadifferentone).That,dividedbythenumberofclassificationsmade,istheerrorrate(usuallyexpressedasapercentage).Theerrorrateisonlywithrespecttotheprobabilitydistributionofthetestcases.

Examples:AfteryouinstallNeticaonyourcomputer,withinthe"Netica"folderwillbeafoldercalled"Examples".ItcontainsseveralBayesnetssuitableforanintroductiontothefieldofBayesnets,andforuseinlearningaboutNetica.Withinitisafoldercalled"Tutorial-Viewthesefirst"containingonorderedsetofBayesnetsthatcontainsometutorialinformationandexercisesintheirnetdescriptionwindow;ifyouareworkingthroughthem,youmightbeinterestedinreadingtheQuickTourofthisonscreenhelp(ifitmentionssomefileyoudon'tseeintheExamplefolder,don'tforgettolookinitsTutorialsubfolder).Formanymoreexamples,besuretoseeourgreatonlineBayesnetlibrary,availablebychoosingHelp→NetLibraryWebsite.

Expectedvalue:Theexpectedvalue(alsoknownas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_mean_value.htm');returnfalse;">meanvalue)isnotthevalueyou“expect”tosee,andusuallyitisn’teventhevaluemostlikelytooccur.Thisterm,fromprobabilitytheory,meanstheaveragevaluethatwilloccur,wheretheaverageisweightedbytheprobabilityofoccurrence.Forexampleifthevaluewillbe3withprobability0.2and9withprobability0.8,thentheexpectedvalueis:(0.2x3)+(0.8x9)=7.8.

Experience:ForlearningandcommunicatingtheknowledgecontainedwithinaBayesnet,itisusefultoindicatea“confidence”intheconditionalprobabilitiesitcontains,sothatoneknowshowmuchtochangethemwhennewinformationaboutthembecomesknown.Thatconfidenceiscalledtheexperience,anditiscalibratedtobeequivalenttoseeingacertainnumberofrelevantcases.Sometimesthisiscalledthe“equivalentsamplesize”.MoreInfo

Explaining-Away:IfAandBarebothpossiblecausesofE,thenwhenwefindthatEoccurred,providingtherearenocomplicatingfactors,ourbeliefsthatAoccurredandBoccurredwillbothincrease.ButifwefurtherdiscoverthatAoccurred,thenourbeliefthatBoccurredwillgobackdownalittle.Thisiscalledexplaining-away,becauseAprovidestheexplanationforE,andthereisnoneedforBtohaveoccurredtoexplainE.Bayesnetsautomaticallyhandleexplainingawayinthecorrectmanner,whileevidence-basedandrule-basedsystemsaregenerallypooratit.

GlossaryF-MFading:WhenaBayesnetisusedinanenvironmentthatischanging,itmaybedesirabletohaveitadapttoitsenvironmentbyconstantlylearning,inaprocessthatweightscasesithasseenrecentlymorestronglythanthoseseeninthefarpast.Theprocessofdiscountingknowledgelearnedfromthepastiscalledfading.MoreInfoFinding:Afinding(alsoknownas“evidence”)isavalueforoneofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodes(i.e.variables)ofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetwhenitisappliedtoaparticularsituation.MoreInfoFindingsmenu:A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretenode’sfindingsmenuisobtainedby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickingonthenode.Itliststhestatesofthenode,andmaybeusedtoentera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">finding.MoreInfoFindingsnode:Afindingsnodeisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodewhichhasa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">finding,orwhich

weknowwillreceiveafindingbeforedoing=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_query_node.htm');returnfalse;">targetnode.Functiontable:Whentherelationshipbetweenanodeanditsparentsisdeterministic,ratherthanprobabilistic,theninsteadofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTanodemayhavefunctiontable,inwhicheachrowcorrespondstoaconfigurationofparentvalues,andtherowprovidesasingleoutputvalueforthechildnode(i.e.thetableisafunctionmappingparentnodetuplestochildnodevalues).IfafunctiontableisconvertedtoaCPT,theneachrowoftheresultingCPTwillconsistonlyofzeroes,withasingle1(or100%)positionedatthestatethatwasthefunctiontable'svalueforthatrow.MoreInfoHomefolder:TheNeticahomefolderisthefolderthattheNeticaexecutable"Netica.exe"appearsin,asdescribedinInstallation.NormallyeachversionofNeticaonyoursystemhasitsownhomefolder.WhenNeticaisrunning,youcandiscoverwhichfolderisthehomefolderbychoosingHelp→Aboutandthenlookingatthelastlineofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Messages_window.htm');returnfalse;">Messageswindow.AlsosometimescalledtheNeticahomedirectory.Hugin:AqualityprogramavailablefromHuginExpertA/SwhichworkswithBayesnetsmuchthesameway=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica.htm');returnfalse;">Neticadoes.Neticacanread.netfilesproducedbyHuginversions4,5or6.

IDname:AnIDnameisanywordthatstartswithasimpleletter(a-zorA-Z),iscomposedonlyofsimpleletters,digitsandunderscores(_),andis30orfewercharacterslong.Itmustnotcontainanyspacesorpunctuation.iff:iffmeans“ifandonlyif”.Sotheexpression“AiffB”canbeinterpretedtomean“ifAthenB,andifBthenA”.Ineffectuallink:Anineffectuallinkisoneinwhichthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTtableofitschildnodecontainthesameprobabilitiesindependentofthestateofthatlink'sparentnode.Inotherwords,thetablecontainsreplicatedchunks,withanidenticalchunkforeachstateoftheparentnode.Ineffectuallinksmayberemovedwithouteffecting=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">inferenceresultsatall.Whenalinkisfirstadded,itisaddedasanineffectuallink,andremainsthatwayuntiltheCPTtablesofitschildnodearemodified.Neticacanfindanddisplayalltheineffectuallinksinanet.Informationallyindependent:AvariableXissaidtobe(informationally)independentofanothervariableYifobtainingknowledgeaboutthevalueofXdoesnotchangeyourbeliefsaboutthevalueofY.IfXisinformationallyindependentofY,thenYisinformationallyindependentofX.Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditionally_independent.htm');returnfalse;">conditionallyindependent.Informationallink:Anylinkenteringa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodeisknownasaninformationallink,andindicatesthatthedecisionmakerwillknowthevalueofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentnodewhenhemustmakethatdecision.Invertiblenode:Aninvertiblenodeisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicnodewhoserelationshipwithitsparentsisinvertible.Thatis,thevalueofanyoneofitsparentsmaybeexpressedasafunctionofitandtherestofitsparents.Jointdistribution:Thejointdistributionprovidesaprobabilityforeverypossibleoutcome(i.e.everyelementofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_cartesian_product.htm');returnfalse;">cartesianproductofallthegivenvariables).Sinceone,andonlyone,oftheseoutcomeswilleventuallyoccur,thejointdistributionprobabilitiesaddto1.Jointprobability:Ajointprobabilityisaprobabilityfromthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_joint_distribution.htm');returnfalse;">jointdistribution.Junctiontree:Ajunctiontree(alsoknownasa“jointree”)istheinternalstructurethatNeticausesfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating.Neticacompilesa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetor=4

&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetintoajunctiontreeforefficiency.MoreInfoLatentnode:Alatentnode(alsoknownasa“hiddennode”)isanodeinalearnedBayesnetwhichdoesnotcorrespondtoanyvariableintheinputdata.Thatis,thevariablewascreatedtomoreeasilyexpresstherelationshipsbetweenobservedvariables.Leafnode:Aleafnodeisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodewithno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_child_node.htm');returnfalse;">children.Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_barren_node.htm');returnfalse;">barrennodeand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_root_node.htm');returnfalse;">rootnode.Likelihoodfinding:Alikelihoodfinding(alsoknownas“virtualevidence”)isa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingwithsomeuncertaintyattached.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativefindingand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positivefinding.MoreInfo

Link:Alink(alsoknownasan“arc”oran“edge”)isaconnectionbetweentwo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodesindicatingdependence,andisusuallydrawnasalinewithanarrowatoneend.MoreInfoLinkreversal:Linkreversalistheprocessofchangingthedirectionofalink,andthenmakingnecessarychangestotherestofthenetsothatanysubsequentinferenceresultswillnotbeaffected.However,itmayresultinlessefficientinference(oroccasionallymoreefficient),sinceextralinksmayhavetobeadded(removed)tomaintaintheglobalrelationshipsbetweenthenodes.MoreInfoLinkstructure:Thelinkstructure(alsoknownasthe“topologicalstructure”or“dependencygraph”)ofaBayesnetordecisionnetisjustthegraphstructureofthenet.Inotherwords,itconsistsonlyofthenodenamesandlinks,butnotofanyotherinformationaboutthenodesortheparticular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationshipsthenodeshavewiththeirparents.Loopcutset:Aloopcutsetforanetisasetofnodessuchthatiftheyareallremovedfromthenet(alongwithalllinksinvolvingthem)therewillbenoloopsinthenet.Seealsocutset.Markovblanket:AsetofnodesBisaMarkovblanketofnodeX,ifgivenfindingsforallthenodesofB,Xisindependentofallothernodesinthenet.Ifitistheminimalsuchset,thenitiscalledtheMarkovboundary(seebelow).Markovboundary:TheMarkovboundaryofanodeXistheminimalsetofnodesforwhichanysetof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_positive_finding.htm');returnfalse;">positive

findingscanbesuppliedandXwillbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditionally_independent.htm');returnfalse;">conditionallyindependentofallothernodesinthenet.ForaBayesnet,thisisX'sparents,X'schildrenandX'schildrens'otherparents.AsetofnodesYcanalsohaveaMarkovboundary.IfpositivefindingsareobtainedfortheMarkovboundarynodes,thenfindingsfortheYnodeswillnotprovideanyadditionalinformationaboutanyothernodeinthenetandvice-versa.NeticacanfindanddisplaytheMarkovboundaryofanodeorsetofnodes.Markovnetwork:AMarkovnetworkisan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_network.htm');returnfalse;">undirectednetworkinwhichthenodesrepresentvariablesofinterestandtheconnectionsbetweenthemrepresentprobabilisticdependence.NeticaconvertsaBayesnetintoaMarkovnetworkasanintermediatestepinproducinga=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontree.MoreInfoMeanvalue:Incalculus,themeanvaluetheoremstates,roughly,thatgivenasectionofasmoothcurve,thereisapointonthatsectionatwhichthederivative(slope)ofthecurveisequal(parallel)tothe"average"derivativeofthesection.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_mean_value.htm');returnfalse;">MoreInfoMessageswindow:TheMessageswindowisawindowthatNeticausestocommunicatetextualinformationtoyou.YoucanopenitanytimeusingWindow→Messages,andyoucancopyandpasteinformationbetweenthe

Messageswindowandanytextfile.Sometimesifyoumakeaminormistake,Neticajustbeepsandplacesamessagethere.MoreInfoMissingdata:Ifsomecaseshavevaluesforacertainvariable,andothersdonot,thatisknownasmissingdata.MoreInfoMoralgraph:Anetinwhicheachnodehasallitsparentsconnectedtoeveryotherofitsparents(i.e.thereareno“illegitimate”children).Moralizinganetconsistsofaddingtherequiredconnectionsbetweenparentsofanodeforallthenodes(i.e.“marrying”them).MostProbableExplanation(MPE):Themostprobableexplanation,orMPE(alsoknownas“maximuma-posterioriprobability”or“MAP”)isasetofvalues(oneforeachnode)thatisthemostprobableconfiguration,giventhenet’scurrentfindings.Sincetheremaybeseveralconfigurationswiththesameprobability,theMPEmaynotbeunique.MoreInfoMultiply-connected:Amultiply-connectednetworkisadirectedorundirectednetworkwhichhasmorethanone=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_path.htm');returnfalse;">undirectedpathbetweensomepairsofnodes.Inotherwords,ithas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_loop.htm');returnfalse;">loops.MoreInfoMultipurposeselector:Whenyouclickonthemultipurposeselector,

,ofanodedialogbox,youwillbepresentedwithamenuofnodepropertiesthatcanbeeditedintheboxbelowtheselector.(MoreInfo)

GlossaryN-RNaturenode:AnaturenodeinaBayesnetrepresentssomevariableofinterest.Itmayalsoappearinadecisionnetinwhichcaseitisavariablethatcannotbedirectlycontrolledbythedecisionmaker(i.e.itisdeterminedbynature).Ifanaturenodehasafunctionalrelationshipwithitsparents,itiscalledadeterministicnode,whereasiftherelationshipisprobabilistic,itiscalledachancenode.Thecharacteristicshapeforanaturenodeisanellipse,orarectanglewithroundedcorners.Negativefinding:Anegativefindingisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingthatsomenodeisdefinitelynotinsomeparticularstate.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">positivefindingand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">likelihoodfinding.MoreInfoNet:InNeticadocumentation,thewordnetisusedtomeana=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnet.Netica:Neticaisaprogramcreatedby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsysforworking

with=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetsand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.MoreInfoNeticaAPI:NeticaAPI(alsoknownas“NeticaProgrammer’sLibrary”)issoftwarethatyoucanlinkwithyourownprogramstoachievemuchofthefunctionalityof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_Application.htm');returnfalse;">NeticaApplication.Itiscreatedby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Norsys.htm');returnfalse;">Norsysandisdesignedforworkingwith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetsand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.MoreInfoNeticaApplication:NeticaApplicationisthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica.htm');returnfalse;">Neticaproductwithaneasy-to-usegraphicalinterfaceforbuildingandworkingwithBayesnetsand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.ToprogramNetica,useNeticaAPIinstead.Netica-Web:Netica-WebisasystemtodeployyourBayesnetsovertheinternetasaquestion-answersystem.Suchasystemaskstheuserquestions,or

providesadashboardtoenterrelevantinformation,andpresentstheuserwithconclusions.MoreinfoNo-forgettinglinks:Ifadecisionmakerremembersthedecisionshemadeatanearliertime,andalsotheknowledgehehadavailabletohimatthattime,theninhisdecisionnettherewillbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_informational_link.htm');returnfalse;">informationallinksgoingfromearlierdecisionnodesandtheirparents,tolaterdecisionnodes.Thesearecalledno-forgettinglinks.MoreInfoNode:AnodeisacomponentofaBayesnetordecisionnetusedtorepresentavariable(i.e.scalarquantity)ofinterest,andinNeticaisusuallydrawnasarectangle,roundedrectangle,circleorflattenedhexagon.MoreInfoNodedialogbox:Tochangeorviewthepropertiesofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">node,suchasitsnameorthestatesithas,youuseanodedialogbox,whichyouobtainbydouble-clickingonthenode,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectingitandthenpressingtheENTERkey.Tochangeitsrelationwithitsparentnodes,youusea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogbox.MoreInfo

Currentstate:Thecurrentstateofa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogbox,isthestatedisplayednexttothelabel“State:”Itmaybechangedbyusingthepopupmenunexttothe“States:”label.

Thestateintervalthresholdsor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_value.htm');returnfalse;">statevaluedisplayedisforthecurrentstate.MoreInfo

nodename:Thenodenametexteditboxinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogboxlookslike=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_node_name.htm');returnfalse;">this.

nodetitle:Thenodetitletextboxinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogboxlookslike=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_node_title.htm');returnfalse;">this..

stateslabel:Thestateslabelinthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogboxlookslike=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_graphic_states.htm');returnfalse;">this.

Noderelationship:Anoderelationship,ornoderelationforshort,isthe

relationshipbetweenanodeandits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parents.Itmayprovidethevalueofthenodeasafunctionofitsparents’values,oritmayprovideaprobabilitydistributionforthenodedependingonitsparents’values.Itisoftenexpressedasa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTinwhichcaseitcanbeviewedoreditedusingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogbox.Alternately,itmaybeexpressedasaprobabilisticordeterministic=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equation.Non-extremeprobability:Anon-extremeprobabilitydistribution(alsoknownas“strictlypositive”)isonewheretheprobabilityisnever0.Thatmeansthatitisalsonever1,andthatithasnopointsofcomplete“certainty”.Normaldistribution:Thenormaldistribution(alsoknownas“Gaussiandistribution),isthemostcommonlyusedcontinuousdistributionwithinfinite=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_support.htm');returnfalse;">support.MoreInfoNormativetheory:Anormativetheorydoesnotindicatewhatagentsusuallydo(whichisadescriptivetheory)orwhatagentsoughttodo(whichisaprescriptivetheory),butwhatagentsmustdoiftheywishtoactoptimallyinagivensituation,whereoptimallyisdefinedinaparticularwaywithrespecttothesituation.Norsys:NorsysSoftwareCorp.isthecompanywhichdevelops=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_Netica_Application.htm');returnfalse;">NeticaApplicationand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPI.YoucangetmoreinformationaboutNorsysfromtheirwebsiteat:www.norsys.com.Questionsandcommentsareverywelcome,andmaybesentbyemail.Optimalpolicy:Theoptimalpolicy(alsoknownasthesetofoptimaldecisions)isthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_policy.htm');returnfalse;">policywhichresultsinthegreatest=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueforthesumofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynodes(oroneofthosepoliciesiftherearemorethanonewhichresultinthesameexpectedutility).Findingtheoptimalpolicyissometimescalled“solving”adecisionnet.Outcome:Theoutcomeistheresultofanevent,orseriesofevents,thatcouldhaveturnedoutinoneofseveralways.Parameterlearning:Parameterlearningistheautomaticlearningofthespecificrelationshipsnodeshavewiththeir=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsusingcasedata,onceithasalreadybeendeterminedwhichnodesaretheparentsofeachnode.Theserelationshipsareusuallyintheformof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobabilities,ortheparametersofaconditionalprobability

equation.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_structure_learning.htm');returnfalse;">structurelearning.MoreInfoParentnode:Ifthereisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">linkgoingfrom=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodeAtonodeB,thenAissaidtobeaparentnodeofB.Somepeoplerefertoitasa“directpredecessor”.Path:Apathisasequenceofnodesfroma=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_net.htm');returnfalse;">net,suchthatyoucangetfromonenodeofthesequencetothenextnodebytraversingalinkbetweenthem(butnotnecessarilyinthedirectionofthearrow).Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_path.htm');returnfalse;">directedpath.Poissonprocess:APoissonprocessisoneinwhicheventsoccurrandomlyandindependentofeachother.ThenumberofeventsthatoccurinafixedtimeperiodisgivenbythePoissondistribution,thetimebetweensuccessiveeventsisgivenbytheexponentialdistribution,andthetimerequiredfortheoccurrenceofafixednumberofeventsisgivenbythegammadistribution.Policy:Apolicy(alsoknownasa“controllaw”)isasetof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_rule.htm');returnfalse;">decisionrules,withoneforeach=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodeofadecisionnet.WhenNetica“optimizesdecisions”itfindsthepolicywhichmaximizesthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueofutility.Positivefinding:Apositivefindingisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingthatsomenodeisdefinitelyinsomeparticularstate.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_negative_finding.htm');returnfalse;">negativefindingand=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_likelihood_finding.htm');returnfalse;">likelihoodfinding.MoreInfoProbabilisticinference:Probabilisticinferenceistheprocessofcalculatingnew=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsforasetofvariables,givensome=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings.Technicallyspeaking,itistheprocessoffindingaposteriordistribution,givenapriordistribution,amodelandsomeobservations.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetsdoprobabilisticinferenceby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating.

Probabilitydensityfunction:Theprobabilitydensityfunction(alsoknownas“pdf”),isafunctionthatprovidestheprobabilityofacontinuousprobabilitydistributionateachpointwithinthedistribution.Itmaybeintegratedoveraregiontodeterminetheprobabilityofthatregion.Itisnowherenegativeanditsintegraloverthewholedistributionisalways1.Theintegralofthepdffromnegativeinfinitytoxisknownasthecumulativedensityfunction(cdf).Probabilityrevision:Probabilityrevisionistheprocessofadjustingthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">conditionalprobabilitytablesofaBayesnettoaccountforanew=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">case(i.e.setoffindings),ormoreoften,foranewsetofcases.Itisaformof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parameter_learning.htm');returnfalse;">parameterlearning,whichgenerallyinvolveslearningfromcases.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating.Prospect:Aprospectistheprobabilitydistributionoverpossible=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_outcome.htm');returnfalse;">outcomes,givena=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_policy.htm');returnfalse;">policyandsome=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings.

Querynode:SeeTargetNode.Relationsymbol:Therelationsymbolisagreentreestructurewhichlookslikethis: Itisusedontoolbarbuttonstoindicatethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationanodehaswithitsparents.Forexample,the buttonistovieworeditatable,the buttonremovesanode’stable,andthe buttonwithadicerandomizesatable.

Reports:Neticacangenerateamultitudeoftextreports,usefulinunderstandingtheinformationinyournet.Thesereportsinclude:

Report→Beliefs,whichliststhecurrentbeliefs(i.e.posteriorprobabilities)fornaturenodes,andexpectedutilitiesfordecisionnodes.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_beliefs.htm');returnfalse;">EXAMPLE

Report→CPTTables,whichliststhenoderelationasaconditionalprobabilitytable(=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPT)or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontable.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_CPT.htm');returnfalse;">EXAMPLE

Report→Elimination,whichliststheorderusedduringcompiling.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_elimination.htm');returnfalse;">EXAMPLE

Report→Equations,whichlistsall=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_equation.htm');returnfalse;">equationsofnodes.ChoosingtheHorizontalFormatoptionprintsthemininternalform.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_equations.htm');returnfalse;">EXAMPLE

Report→Excel,whichhot-linkstothenodebeliefs.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_excel.htm');returnfalse;">EXAMPLE

Report→Findings,whichliststhe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findings(i.e."case"or"evidence")currentlyentered,includinglikelihood("virtual")findings.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_findings.htm');returnfalse;">EXAMPLE

Report→JunctionTree,givesdetailsofthenetcompilationprocess.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_junctiontree.htm');returnfalse;">EXAMPLE

Report→ListSelected,generatesalistofthenamesofthenodescurrentlyselected.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_listselected.htm');returnfalse;">EXAMPLE

Report→NodeSets,whichliststhenodeswithintherequestedset.=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_nodesets.htm');returnfalse;">EXAMPLE

Report→Network,whichgivesasummaryinformationonthewholenet.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_report_whole.htm');returnfalse;">EXAMPLE

Retracted:Anytimeaftera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findinghasbeen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteredintoanode,thatfindingmayberemoved,orretracted.Afterdoingbeliefupdatingforthenet,itwillbeasifthefindinghadneverbeenentered.MoreInfoRight-click:Toright-clickonsomething,placethemousepointer("cursor")overit,thenpresstherightmousebuttonandchooseanitemfromthemenuthatcomesup.MoreInfoRootnode:Arootnodeisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodewithno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parents.Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_leaf_node.htm');returnfalse;">leafnode.

GlossaryS-ZSelectlink:Inordertodosomeoperationsona=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">link,youfirstselectitbyclickingonceonit,anditwillthenbedrawnusingnegativecolorstohiliteit.Toselectmorethanonelink,orremovelinksfromyourselection,holddowntheCTRLkeywhileclickingonthem.MoreInfoSelectnode:Inordertodosomeoperationsona=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">node,youfirstselectitbyclickingonceonit,anditwillthenbedrawnusingnegativecolorstohiliteit.Youcanselectseveralnodesatatimebyclickingonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_background.htm');returnfalse;">backgroundanddraggingtheselectionrectangletoincludethem.Toaddorremovenodesfromyourselection,holddowntheCTRLkeywhileyoudotheselectionoperation,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_right_click.htm');returnfalse;">right-clickonthenodeandchooseSelect/Deselect.MoreInfoSingly-connected:Asingly-connectednetworkisadirectedorundirectednetworkthathasatmostone=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_path.htm');returnfalse;">undirectedpathbetweenanytwonodes.Inotherwords,ithasno=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_loop.htm');returnfalse;">loops.MoreInfo

Standarddeviation:Thestandarddeviationisthesquarerootofthevariance.ItsunitsarethesameasthoseofX,anditisameasureofhow“spreadout”or“imprecise”thedistributionis.MoreInfoStatelevel:When=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretizingacontinuousvariable(i.e.node),asetofnumericbordersisusedtopartitiontherangeofthevariableintointervalscalledstates.Thosebordersarecalledthresholds.Eachstateofthediscretizedvariablehasalowerthresholdandanupperthreshold,withtheupperthresholdbeingthesameasthelowerthresholdofthenextstate.Ifreferenceismadetoastate'sthresholdwithoutspecifyinglowerorupper,thenlowerisimplied,anditisalsosometimesreferredtoasthestate'slevel.Statevalue:Any=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete_node.htm');returnfalse;">discretenodemayhaveassociatedwitheachofits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">statesanumber(integerorreal)calleditsstatevalue,whichmaybeusedtoidentifythatstateindatabasesorcasefiles,ormaybeusedtoprovidean"outputvalue"forthatstateinequations.=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_continuous.htm');returnfalse;">Continuousnodesdon'thavestatevalues,butiftheyhavebeen=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discretize.htm');returnfalse;">discretized,theyhavestate=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state_threshold.htm');returnfalse;">thresholdsinstead,andsometimesthetermstatelevelisusedtorefertonumbersthatare

statevaluesorthresholds.MoreInfoStates:A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretevariablecantakeononeofseveralvalues,andthesevaluesarecalledstates.Forexamplethestatesmaybe“female,male”,ortheymightbe“US,Europe,Japan,China”,or“True,False”.WithNeticayoucanjustletthestatesofanodebenumbered,butusuallyyougivethemmeaningfulnames.Structurelearning:Structurelearningistheautomaticdiscoveryofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructureofaBayesnetfromcasedata.Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parameter_learning.htm');returnfalse;">parameterlearning.Support:Thesupportofaprobabilitydistributionistherangeofitsvariable(s)overwhichthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_pdf.htm');returnfalse;">pdfisnonzero.Inotherwords,thosevaluesofthevariablewhicharepossible.Tabdelimitedtextfile:Tabdelimitedtextfileisacommonlyusedtermforaformofcasefileinwhichthenamesofthevariablesappearonthefirstline,andthenbelowareallthecases(i.e.records),witheachcaseonasinglelineandhavingavalueforeachofthevariables,andwithallthevaluesandvariablesintextformandseparatedbytabcharacters.Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CSV_file.htm');returnfalse;">CSVfile.Tabledialogbox:Tochangeorviewtherelationshipofa=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node.htm');returnfalse;">nodewithits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentsthatis,edititsconditionalprobabilitytable(CPT)or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_function_table.htm');returnfalse;">functiontable,youuseatabledialogbox.Toobtain=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_select_node.htm');returnfalse;">selectthenode,andthenchooseTable→View/Editorclickthe toolbarbutton.Itisnottochangethenode'sbasicproperties;forthat,usea=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_dialog_box.htm');returnfalse;">nodedialogboxinstead.MoreInfo

Tableselector:Withinthetabledialogbox,youwillfindatableselector,whichlookslike=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_selector.htm');returnfalse;">this,andwhichprovidesamenuforyoutoselectthetypeoftablethatyouview.

TargetNode:Atargetnodeisanodewhosebeliefswewanttoknowafterbeliefupdating.Alsoknownasa"querynode".Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_findings_node.htm');returnfalse;">findingsnode.

Testsensitivity:Thetestsensitivityofanimperfecttestisthepercentageofcasestestingpositiveoutofthosethatshouldtestpositive.Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"

onclick="BSSCPopup('X_PU_test_specificity.htm');returnfalse;">testspecificity.Testspecificity:Thetestspecificityofanimperfecttestisthepercentageofcasestestingnegativeoutofthosethatshouldtestnegative.Seealso=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_test_sensitivity.htm');returnfalse;">testsensitivity.Texteditor:AtexteditorisaprogramthatallowsyoutomodifyplainASCII=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_file.htm');returnfalse;">text.ForsmallfilesyoucanuseNetica’sFile→New→TextEditorFile→OpenasText.ForlargerfilesyoucanuseawordprocessingprogramsuchasMSWordorWordPad(saveas“TextOnly”ifyouwishtomakeafile).Textfile:Atextfileconsistsonlyof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_ASCII.htm');returnfalse;">ASCIIcharacters.Ithasnospecialsymbols,noformatting(bold,italics,fontsorsizes),nostructure(paragraphsections,chaptersections,margins,etc.),andnospecialinserts(pictures,tables,etc.).Youcancreateormodifyatextfileusinga=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_text_editor.htm');returnfalse;">texteditor.Time-delaylink:Atime-delaylinkisalinkwhichindicatesthatthechildnodeisforavariable'svalueatapointintimelaterthanthevalueofthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_parent_node.htm');returnfalse;">parentnodeonwhichitdepends.Thetimedifferenceissomethingthatyoucansetforthelink.Anetthatcontainstime-delaylinksisnotanormalBayesnet,butrather

ameta-levelrepresentation,butitcanbeexpandedtoproduceanormalBayesnet.Timedelaylinkscanbeusedtomodelfeedback.MoreInfoToggled:Amenuitemthatcanbetoggledislikeaswitchthatcanbeturnedonandoff.Whenyouchooseit,acheckmarkwillappearbesideit,indicatingitison.Choosingitagainwillremovethecheckmark,indicatingitisoff.Triangulated:An=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_network.htm');returnfalse;">undirectednetworkistriangulatedifeveryloopoflength4ormorehasachord,i.e.alinkjoiningtwononconsecutivenodes.Triangulatinganetistheprocessofaddinglinksuntilitistriangulated(whichmaybedoneindifferentways,dependingonwherethelinksareadded).Theresultingnetiscomposedonlyoftriangles(eachsidebeingalink)fusedtogetheralongtheirsides.Undirectedloop:Anundirectedloop(sometimesjustcalleda“loop”)isa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_path.htm');returnfalse;">paththroughanet,notnecessarilyfollowingthedirectionofthearrows,whichreturnstoitsbeginning(i.e.thefirstnodeofthepathisthesameasthelast).Comparewith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_cycle.htm');returnfalse;">directedcycle.Undirectednetwork:Anundirectednetworkisonewherethelinkshavenodirection(i.e.noarrows).A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Markov_network.htm');returnfalse;">Markovnetworkisanexample.Comparewitha=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_directed_network.htm');returnfalse;">directed

network.Unicode:Unicodeisatextcharactersetthatwasdesignedwiththegoalofbeingabletorepresentallthecharactersofalltheworld'slanguages.Itisbyfarthedominantinternationalcharacterset,andwasdevelopedbyaconsortiumwithmostofthelargestcomputercompaniesasmembers.Thefirstversionwasreleasedin1991,andabouteveryyearanewversionisreleasedhavingmorecharacters.Itnormallyrepresentseachcharacterwith2bytes,althoughthereareanumberofcomplexitiesandalternateencodings.NeticaallowssomeaspectsofBayesnetstoberepresentedinUnicode,whileothersarerequiredtobein=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_ASCII.htm');returnfalse;">ASCII.Userreports:aNeticamechanismwhichdisplayscustomizedinformationpertainingtoanode,groupofnodes,ortoanentirenet.Theuserreportcouldbeassimpleasatextmessagegivingamoredetaileddescriptionofwhatanodemeans.Oritcouldbemorecomplex,suchasthecurrentbeliefprobabilitiesofthenodes,orasensitivityanalysisofthenet.UserreportscanalsobegeneratedthroughtheHEDsystem.Utilitynode:Autilitynode(alsoknownasa“valuenode”)isanodeina=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetwhose=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_expected_value.htm');returnfalse;">expectedvalueistobemaximizedwhilesearchingforthebest=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_rule.htm');returnfalse;">decisionruleforeachofthedecisionnodes.Itisusuallydrawnasaflattenedhexagonoradiamond.Weaklink:Theabsenceofalinkalwaysindicatessome=4&&

typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_info_indep.htm');returnfalse;">independence,butevenifalinkispresenttheremaynearlybeindependenceifthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_node_relation.htm');returnfalse;">relationshipthatthechildnodehaswithitsparentsindicatesthat.Thenitiscalledaweaklink.Removingaweaklinkhaslittleeffectonthefulljointprobabilitydistribution,andthereforelittleeffectoninferenceresults.Whitespace:Whitespaceistextwhichiscomposedsolelyofspaces,tabs,newlines,carriagereturnsorotherasciicontrolcharacters.

EncyclopediaAxiomsofProbabilityTheory

BayesTheorem

CartesianProduct

ConditionalProbability

Connectivity

d-separation

Discretevs.Continuous

FundamentalTheoremsofProbability

GameTheory

JunctionTree

Link

MarkovNetwork

MessagesWindow

Node

Password

ProbabilisticInferencebyNodeAbsorption

StandardDeviation

AxiomsofProbabilityTheoryHereisasetofaxiomsforprobabilitytheoryequivalenttothosederivedbyCox(andalsocompatiblewithotheraxiomatizationsofprobability,suchastheKolmogorovaxioms):

whereP(x,y|z)meanstheprobabilitythatpropositionsxandyarebothtrue,giventhatpropositionzistrue.

BayesTheoremForanytwopropositions,AandB,P(B|A)=P(A|B)xp(B)/p(A),whereyouread'PP(A)'as"theprobabilityofA",and'P(A|B)'as"theprobabilityofAgiventhatBhasoccurred".

Asshown,Bayesrulefollowsdirectlyfromthedefinitionofconditionalprobability.Thistheoremisawaytotranslatebetweentheprobabilityofcauses,giveneffectsandtheprobabilityofeffectsgivencauses.

CartesianProductThecartesianproductoftwosetsisthesetofallpossiblepairsofelements,wherethefirstelementofeachpairistakenfromthefirstset,andthesecondelementistakenfromthesecondset.Forexample,thecartesianproductof{low,medium,high}with{true,false}is{(low,true),(low,false),(medium,true),(medium,false),(high,true),(high,false)}

Thecartesianproductisdenotedusing‘x’.Itmaybeextendedtomorethantwosets,asshowninthissecondexample:

{s1,s2}x{s,h}x{wtg,mhc}={(s1,s,wtg),(s1,s,mhc),(s1,h,wtg),(s1,h,mhc),(s2,s,wtg),(s2,s,mhc),(s2,h,wtg),(s2,h,mhc)}

Thenumberofelementsinthecartesianproductisthemultiplicativeproductofthesizesofthesetsinvolved.Inthefirstexampleitis3*2=6,andinthesecondexampleitis2*2*2=8.

SomepeoplespellitwithacapitalC(“Cartesianproduct”),sinceitisnamedafterDescartes.

ConditionalProbabilityTheprobabilitythatsomespecifiedvariables(calledthehypothesisvariables)takespecifiedvalues,giventhatsomeotherspecifiedvariables(calledthegivenvariables)havespecifiedvalues.Theremaybeanynumberofgivenvariables,includingnone(inwhichcaseitsalsocalledapriorprobability).Ifthevaluesofthegivenvariablesareinconsistent(i.e.theirprobabilityofoccurringtogetheris0),thentheconditionalprobabilityisundefined.

ConnectivityThe“connectivity”ofanetreferstoanet’s=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructure.Highconnectivitymeansthattherearealotoflinks.

Youcanusethelinkstructureofanettodetermineindependencebetweennodes,byusingthed-separationalgorithm.

AMultiply-Connectednetisanetwhichhasmorethanone=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_path.htm');returnfalse;">undirectedpathbetweensomepairsofnodes.Inotherwords,ithas=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_loop.htm');returnfalse;">loops.

ASingly-Connectednetisanetthathasatmostonepathbetweenanytwonodes.Inotherwords,ithasnoloops.Ifthelinkdirectionsareignored,itisalwayspossibletoconsideritasatree.Ifthelinkdirectionsarenotignored,thensomepeoplecallita“polytree”(becauseitcanbeconsideredtobeseveraldirectedtrees,witharrowsfromroottoleaves,fusedtogetheratleafnodes).

ThetimeittakesforNeticatodo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdatingisverydependentontheconnectivityofthenet.Addingalinkalwaysresultsinlongerupdatingtimes,butwherethatlinkisaddedcanmakeabigdifference.Ifanodehasmanyparents,thenits=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditional_probability.htm');returnfalse;">conditionalprobabilitytablewillbeverylarge,whichresultsinsloweroverallupdatingtimes.Thenumberofloopsanethasisalsoverysignificant.Ifanethasnoloops,thenNeticacandoupdatingextremelyfast,andeach

addedloopwillincreasetheupdatingtime.

Neticaimplementsanumberofgraphalgorithmstomakevariousconnectivityresultsavailabletoyou,suchasfindingallparents,children,ancestors,descendents,connected,d-separated,Markovboundary,interconnectinglinks,cycles,etc.MoreInfo

d-separationThed-separationruleenablesyoutoquicklydeterminewhethera=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingatonenodecanpossiblychangethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief.htm');returnfalse;">beliefsatanotherbyonlylookingatthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructureofaBayesnet.

Neticausesd-separationinternally,andcanalsofindanddisplayd-separatednodes.

Discretevs.ContinuousAdiscretevariableisonewithawelldefinedfinitesetofpossiblevalues,called=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_state.htm');returnfalse;">states.Examplesare:thenumberofdimesinapurse,astatementwhichiseither“true”or“false”,whichpartywillwintheelection,thecountryoforigin,voltageoutputofadigitaldevice,andtheplacearoulettewheelstops.

Acontinuousvariableisonewhichcantakeonavaluebetweenanyothertwovalues,suchas:indoortemperature,timespentwaiting,waterconsumed,colorwavelength,anddirectionoftravel.Adiscretevariablecorrespondstoadigitalquantity,whileacontinuousvariablecorrespondstoananalogquantity.

WithNeticayoucanchoosewhetheryouwantanodetorepresentadiscreteorcontinuousvariable.

Oftenavariablewillbecontinuousatonescale,butdiscreteonanother.Forinstancetheamountofwaterconsumedmightbediscreteifyoucountindividualwatermolecules,butitiscontinuousatthescaleyouareconcernedwith.Likewise,thevoltageoutputofadigitaldevicemightbediscreteatthescaleyouareconcernedwith(“high”&“low”),butcontinuousonafinerscale(0.7-3.5V),andthendiscreteonaveryfinescale(correspondingtothenumberofelectronsonacapacitor).Youonlyneedconsiderthescaleofinterestwhensettingwhetheranodeiscontinuousordiscrete.

Sometimesyouwantacontinuousvariabletobehavelikeadiscreteone.Todothis,youbreakupthetotalrangeofthecontinuousvariableintoanumberofintervalsbysupplyingnumbersshowingwhereoneintervalendsandthenextbegins.Thisisknownasdiscretizingthevariable,andthenumbersarecalledthresholds.Eachintervalcorrespondstoonestateofthediscreteversionofthevariable.Adiscretizedvariableissometimesknownasanintervalvariable,sinceitsdomainiscomposedofintervals.InNetica,asinglenoderepresentsboththecontinuousanddiscreteversionsofthevariable,andNeticawillconvertavalueofthecontinuousvariableintoadiscretestatewhenappropriate.Neticaallowsyoutodiscretizeanycontinuousnode,bychoosingModify→DiscretizeNodes.(Ifthevariableis=4&&typeof(BSPSPopupOnMouseOver)=='function')

BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_discrete.htm');returnfalse;">discretethenthemenuwon'thavea"Discretization"choice).

Conversely,adiscretenodemayhavenumericquantitiesattachedtoeachstate,sothateachstatecanrepresentanumber,butthevariableisincapableofrepresentingnumbersbetweenthoseofeachstate(moreinfo).

SeeAlso:NodeDiscretization-Multi-PurposeBox

SeeAlso:NodeStateInterval

FundamentalTheoremsofProbability

BayesTheorem:

Reasoningbycasestheorem:

Independencetheorem:

Whereindependenceisdefinedas:

Ineachoftheabovetheorems,alltheprobabilitiesareconditionedontheproposition.Sinceitcouldbeequivalenttoanylogicalformula,theyallholdwithcreplacedbyanyvectoroftruthvalues,c.

GameTheoryGametheoryusuallyattemptstodeterminewhatwillhappenwhentwoormoreagentscooperate/competeintryingtomaximizetheirownexpectedutility.

Decisiontheoryprescribeshowoneagentshouldbestmakedecisionstomaximizehisexpectedutility,givenhisbeliefsabouttheenvironmentandhowotheragentswillact.

Ifyouspecifythebehavior(asaprobabilisticpolicy)oftheotherplayersinvolvedinagame,thenyoucanusedecisiontheorytodeterminehowoneplayershouldbestact.Butitwon’tdeterminethepoliciesforallplayerssimultaneouslylikegametheorysometimeswill.CurrentlyNeticaonlysolvesdecisiontheoryproblems.Itcanstillbeavaluabletoolforinvestigatinggametheoryproblems,butonlyfromoneplayer'spointofview(ratherthanaglobalpointofview).

IfyouwanttouseNeticatoformulateagame,thenmakeadecisionnodeforasingleplayeranda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenodeforeachoftheotherplayers.Usethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_table_dialog_box.htm');returnfalse;">tabledialogboxtoenterapolicyforeachoftheotherplayers.Therewillbe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link.htm');returnfalse;">linksbetweenthesenodesonlyifsomeplayerswillknowwhatsomeotherplayersactionsarebeforemakingtheirowndecision.

Thenadda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynode,withlinksfromeachoftheothernodestoit.Youcanfilltheutilitynodetablequiteeasilyfromthegametheorypayoffmatrix(itwillhaveonerowforeachcellofthematrix)bykeepinginmindthatyouareonlyenteringthepayofffor

thesingleplayeryouareanalyzing.Supposedlytheotherpayoffswereusedtodeterminethepoliciesfortheotherplayers,perhapsusinganotherdecisionnet.

Youmayfindthatyouwanttoiteratesolutions,sincedevelopingeachplayer'sdecisionnetdependsonthepoliciesofotherplayers,whichyoudon'tknowuntilyouhavesolvedtheirdecisionnets,whichrequirethepolicy(solution)ofthefirstnet.Youmayfind=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Netica_API.htm');returnfalse;">NeticaAPIusefultowriteaprogramforsuchiterations(ortoexplorehowstrategiesandpoliciesofapopulationevolveovertime).

JunctionTreeAlsoknownasa“jointree”.

AjunctiontreeistheinternalstructurethatNeticausesfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating.Neticacompilesa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bayes_net.htm');returnfalse;">Bayesnetor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnetintoajunctiontreeforefficiency.

ThejunctiontreeTof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_triangulated.htm');returnfalse;">triangulatednetGisatreewiththe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_clique.htm');returnfalse;">cliquesofGasnodes,suchthatforeverynodeNofG,ifweremovefromTallcliquesnotcontainingN,theremainingsubtreeremainsconnected.Inotherwords,anytwocliquescontainingNareeitheradjacentinTorconnectedbyapathmadeentirelyofcliquesthatcontainN.

YoucanexaminethejunctiontreethatNeticacreatesforaBayesnetbymakingatextreportusingReport→JunctionTreeaftercompiling.

LinkThelinksofaBayesnetindicatewhichnodes(i.e.variables)aredirectlydependentonothers.Moreaccurately,theyindicatewhichnodesare=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_conditionally_independent.htm');returnfalse;">independentofwhichothers.Ifthereisnolinkfromonenodetoanother,thentheircorrespondingvariablesareconditionallyindependentgivenvaluesfortheirparents.Usingthed-separationrule,youcandeterminewhichnodeseffectwhichothersduringprobabilisticinference,basedonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_link_structure.htm');returnfalse;">linkstructurelinkofthenet.

Alinkbetweentwonodesisindicatedasalinebetweenthemwithanarrowatoneend,thereareseveralwaystoaddlinksbetweennodes.

Alinkintoadecisionnodeisknownasan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_informational_link.htm');returnfalse;">informationallink,andindicatesthatthedecisionmakerwillknowthevaluesoftheparentnodeswhenadecisionmustbemade.

Somepeoplerefertolinksas“arcs”or“edges”.

MarkovNetworkAMarkovnetworkisan=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_undirected_network.htm');returnfalse;">undirectednetinwhichthenodesrepresentvariablesofinterestandtheconnectionsbetweenthemrepresentprobabilisticdependence.NeticaconvertsaBayesnetintoaMarkovnetworkasanintermediatestepinproducinga=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontree.

MessageswindowWhenyoufirststartNetica,inthelowerleftcorneroftheworkspacewhichopenstherewillbeaniconforaminimizedwindowcalled“NeticaMessages”.YoucandoubleclickittoviewitscontentsoryoucanchooseWindow→Messages.Toreturnittoitsminimizedstateclickonthe buttoninitstitlebar.

Note:ifyouareusingNeticaonaMac,theMessageswindowmayappearaseitherablankwhitesquareinthebottomleftoftheNeticawindow,orasjustawordintheupperleftofthescreen.SimplyclickonthesquareorwordtolaunchtheMessageswindow.

Neticareportstextualinformationtoyouthroughthiswindow.IfyoudoReport→Network,thenthereportwillbeplacedintheMessageswindow,andaftercompilinganet,informationonthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_junction_tree.htm');returnfalse;">junctiontreewillbeintheMessageswindow.ProgressduringlengthyoperationsissometimesdisplayedintheMessageswindow,althoughithastobevisiblebeforetheoperationisstarted.

UsuallywhenyoutrytodoanoperationthatNeticacan’tperform,itwilldisplayadialogboxtellingyou.However,forsomeminoroperations,likeclickinginthewrongplace,Neticawilljustbeep.Inthatcase,youcanlookintheNeticaMessageswindowandtherewillbeanexplanation.

YoucancopyandpasteinformationbetweentheMessageswindowandanytextfile.Inaddition,allinformationgoingtothemessageswindowcanalsobesenttoatextfilebychoosingFile→LogMessages.

NodeTherearethreekindofnodesindicatingwhatourintentionisforavariable:=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_nature_node.htm');returnfalse;">naturenodes,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_node.htm');returnfalse;">decisionnodes,and=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_utility_node.htm');returnfalse;">utilitynodes.Anaturenodeissometimescalleda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_chance_node.htm');returnfalse;">chancenodewhenitsrelationshipwithitsparentsisprobabilistic,anda=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_deterministic_node.htm');returnfalse;">deterministicnodewhenitisn’t.Naturenodesmayalsobecalled=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_query_node.htm');returnfalse;">targetnodesifweareinterestedintheirbeliefsafterbeliefupdating,or=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_findings_node.htm');returnfalse;">findingsnodesifwehave,orwillhave,afindingforthem.

PasswordThepasswordyouwereissuedafterpurchasingaNeticaproductcontains5components:yourname,organization,productnumber,versionnumberandasecuritynumber,inthefollowingform:

+Name/Organization/Product-Version-License/Security

TheproductwillbeeitherNeticaApplication(120),NeticaAPI(310),orboth(120,310).Theversionnumberwillbeaninteger,andyourlicensewillbeoneormoreof:commercial(noentry),academic(A),site(S),etc.

HerearesomesampleNeticalicensepasswords:

+MyName/ABCCorp/120,310-2/12345

^theversionnumberis2.

+MyName/DEFUniv/120-1-AS/54321

^theversionnumberis1.

Youwillneedtoenterapasswordaspartoftheinstallationprocess.

StandardDeviationThevarianceofavariableXwithprobabilitydistributionp(x)isgivenby:

where isthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_mean_value.htm');returnfalse;">meanvalue.Thevarianceofaprobabilitydistributionisn’texactlythesameas“samplevariance”,whichisthevarianceofasetofmeasurements.Thestandarddeviationisthesquarerootofthevariance.ItsunitsarethesameasthoseofX,anditisameasureofhow“spreadout”or“imprecise”thedistributionis.Foranydistribution,themean(i.e.,theexpectedvalue)andthemediancanneverdifferfromeachotherbymorethanonestandarddeviation.Fora=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_normal_distribution.htm');returnfalse;">normaldistribution,31.8%oftheprobabilityisoutsideof1standarddeviationfromthemean,4.6%isoutsideof2standarddeviations,and0.26%isoutsideof3standarddeviations.Foranydistribution,lessthan1/(k^2)oftheprobabilityisoutsideofkstandarddeviations(Chebyshev’stheorem).

NeticaAPITheNeticaAPIisacompletelibraryoffunctionsforworkingwithBayesnetsandinfluencediagramsthatyoucancallfromyourownprogram.Itcontainsfunctionstobuild,learn,modify,transform,saveandreadnets,aswellasapowerfulinferenceengine.ThereareversionsofNeticaAPIavailableformanydifferentprogramminglanguages,suchasJava,C,C++,C#,VisualBasic,etc.FormoreinformationontheCOMversionofNeticaAPI(mostlyforC#andVisualBasic),seeNeticaCOMInterface,andforotherversionsseewww.norsys.com/netica_api.html

AnexcitingnewadditiontoNeticaAPIallowsittotakeadvantageoftheNeticaApplicationuserinterfacefordisplayingnets,enteringfindings,showingbeliefs,etc.MoreInfo.

ProgramsthatusetheNeticaAPIcompletelycontrolit.Forexample,Neticafunctionswillnottakeanyactionuntilcalled,NeticawillnotdoanyI/Ounlessrequestedto,anditsfunctionswillnottakeanunpredictableamountoftimebeforereturning.

ItmaybeusedinconjunctionwithotherCorC++libraries(anditwon'tinterferewiththem),butitdoesn'trequireanyotherlibraryexcepttheStandardClibrary.VersionsoftheNeticaAPIareavailableforMSWindows,Linux,SunSparc,SiliconGraphics,MacintoshandDOS,andeachofthesehasanidenticalinterface,soyoucanmoveyourcodebetweentheseplatformswithoutchanginganythingtodowiththeNeticaAPI.

BeforereleasinganynewversionofNeticaAPI,itisputthrougharigoroustestingprogramtomakesureitoperatesasdesigned.Everyfunctionisexercisedinmultipleways,anditsbehaviorcarefullychecked.Thousandsofrandomnetsaregeneratedandsolvedinmultiplewaystochecktheinferenceresults,andhundredsofrealnetsaretested.MemCheck™andPurify™areusedtomakesuretherearenomemoryleaksorothermemoryfaults.Incombinationwithacarefulinitialdesign,andbasesoftwarehavingtenyearsofextensivecustomerusage,thisresultsinarocksolidproduct.

TheNeticaAPIhasbeendesignedtobeeasilyextendedinthefuturewithoutchangingwhatalreadyexists.Manynewfeaturesarecurrentlyunderdevelopment,anditwillcontinuetobeextendedforyearstocome.

Features:•DynamicConstruction:Canbuildandmodifynets"onthefly"inmemory(tosupportworkingwithdynamicBayesnets),andcansave/readthemtofile.

•Equations:Probabilitytablesmaybeconvenientlyexpressedbyequations,usingaJava/Ctypesyntaxandtakingadvantageofanextensivelibraryofbuilt-infunctions,includingallthestandardmathfunctionsandcommonprobabilitydistributions,aswellassomefunctionsanddistributionsspeciallysuitedtoBayesnets,suchasnoisy-or,noisy-max,noisy-sum,etc.

•LearningfromData:Probabilitytablescanbelearnedfromcasedata,evenwhilethenetisbeingusedforprobabilisticinference.Learningfromdatacanbecombinedwithmanualconstructionoftablesandrepresentationbyequations.Itcanhandlemissingdataandlatentvariablesorhiddennodes.Learningalgorithmsinclude:counting,sequentialupdating,fractionalupdating,EM(expectationmaximization),andgradientdescent.

•DatabaseConnectivity:Allowsdirectconnectiontomostdatabasesoftware.

•Threadsafe:Canbeusedsafelyinmulti-threadedenvironments.•Encryption:Cansaveandreadnetstofileinencryptedform,whichallowsdeployingsolutionsrelyingonBayesnetskeptprivatetoanorganization.

•Sensitivity:Neticacanefficientlymeasurethedegreetowhichfindingsatanynodecaninfluencethebeliefsatanothernode,giventhefindingscurrentlyentered.Themeasurescanbeintheformofmutualinformation(entropyreduction),ortheexpectedreductionofrealvariance.

•AdvancedDecisionNets:Cansolveinfluencediagramswhichhavemultipleutilityanddecisionnodestofindoptimaldecisionsandconditionalplans,usingajunctiontreealgorithmforspeed.Handlesmulti-stagedecisionproblems,wherelaterdecisionsdependontheoutcomesofearlierones,andonobservationsnotinitiallyknown.No-forgettinglinksneednotbeexplicitlyspecified.

•JunctionTreeAlgorithm:CancompileBayesnetsandinfluencediagramsintoajunctiontreeofcliquesforfastprobabilisticinference.AneliminationordercanbespecifiedorNeticacandetermineoneautomatically,andNeticacanreportontheresultingjunctiontree.

•SoftEvidence:Acceptslikelihoodfindings(i.e.,“virtualevidence”),and

findingsoftheformthatsomevariableisnotissomestate.•LinkReversal:Canreversespecifiedlinksor"sumout"(absorb)nodesofaBayesnetorinfluencediagramwhilemaintainingthesameoveralljointprobabilitydistribution,properlyaccountingforanyfindingsintheremovednodesorothernodes.

•DisconnectedLinks:Linksmaybeindividuallynamedanddisconnectedfromparentorchildnodes,thusmakingpossiblelibrariesofnetfragments,whichyoumaythencopyandconnecttoothernetsornodeconfigurations.

•CaseSupport:Cansaveindividualcases(i.e.setsoffindings)tofile,andmanipulatefilesofcases.Casesmaybeincomplete,andmayhaveanassociatedIDnumberandmultiplicity.

•Simulation:Candosampling(i.e.simulation)togeneraterandomcaseswithaprobabilitydistributionmatchingtheBayesnet.Canuseajunctiontreealgorithmforspeed,ordirectsamplingfornetstoolargetogenerateCPTsorajunctiontree.

•UserData:Everynodeandnetcanstorebynamearbitrarydatafieldsdefinedbyyou.Thesearesavedtofilewhentheobjectinquestionisbeingsaved.Aswell,therearefieldsnotsavedtofile,whichcancontainapointertoanythingyouwish.

•ErrorHandling:Hasasimplebutpowerfulmethodforhandlingusageerrors,whichcangenerateverydetailederrormessagesifdesired.Itwon’tthrowexceptions(C++versiondoes).

•ArgumentChecking:AllowsprogrammerstocontrolhowcarefullyAPIfunctionschecktheirargumentswhentheyarecalled,includinga"developmentmode"toextensivelycheckeverythingpassedtoanAPIfunction.

•Compatibility:Canworkhand-in-handwithNeticaApplicationstandaloneproduct(forexample,sharingthesamefiles),andwithNeticaAPIversionsforotherlanguages.

•Efficient:Isoptimizedforspeed,andisnottoolarge(about500KBto3MBdependingonplatform/usage,1MBtypical)

•LanguageInterface:Usablebyprogramswritteninmanylanguages,suchas:C,C++,Java,Python,Perl,VisualBasic,DelphiPascal,Lisp,CLisp,Fortran,Cobol,andMatlab.

•ManyPlatforms:IsavailableforawiderangeofplatformsincludingMS

Windows(95/NTtoXP),Linux,Macintosh(OSXandClassic),SunSparc,SiliconGraphicsandDOSamongothers.

•MemoryLimiting:YoucansetaboundonhowmuchtotalheapspaceNeticaAPIisallowedtoallocateforlargetables,therebypreventingvirtualmemorythrashingorthememory-starvingofotherpartsofyourapplication.

•MoreFeatures:Amoreextensivelistoffeaturesisavailablefrom:http://www.norsys.com/netica_api.htmlandforthosefeaturesspecifictotheCversion:http://www.norsys.com/netica_c_api.htm

LegalitiesBeforeinstallingorusingNetica,besurethatyouaccepttheLicenseAgreement,whichisprovidedwiththesoftwareonaseparatedocument(entitledLicenseAgreement.pdf).

Thisentiredocument(consistingofallscreensinNetica'shelpfile)is:

Copyright©1996-2011byNorsysSoftwareCorp.

Thisfilemaybecopiedandstoredfreely,provideditisduplicatedinitsentirety,withoutmodification,andincludingthecopyrightnotice.

NorsysSoftwareCorp.3512West23rdAve.Vancouver,BC,CanadaV6S1K5www.norsys.com

Whileeveryprecautionhasbeentakeninthepreparationofthisdocument,weassumenoresponsibilityforerrorsoromissions.Neitherisanyliabilityassumedfordamagesresultingfromtheuseoftheinformationcontainedherein.

NeticaandNorsysareregisteredtrademarksofNorsysSoftwareCorp.

MicrosoftandWindowsareregisteredtrademarksofMicrosoft,Inc.

iOSisatrademarklicensedtoAppleComputer,Inc.andMacintoshandMacOSareregisteredtrademarkofAppleComputer,Inc.

UNIXisaregisteredtrademarkofTheOpenGroup.

LinuxisaregisteredtrademarkofLinusTorvalds.

UnicodeisatrademarkofUnicode,Inc.

Intelisaregisteredtrademark,andPentiumisatrademarkofIntelCorporation.

Otherbrandsandproductnamesaretrademarksoftheirrespectiveholders.

NeticaApplicationHelpTofindoutmoreaboutanyofthesubjectsbelow,clickonitandthenusetheNext/Previousbuttonsinthenavigationpaneabovetoreadsubsequentpages.Foratableofcontents,index,orfulltextsearchclickontheappropriatebuttonabove.

•GettingStarted•QuickTour•UsingBayesNets•CreatingBayesNetsandDecisionNets•ChangingNodeProperties•Changing/ViewingNodeTables•CasesandCaseFiles•LearningFromCases•TestNetwithCases•Sensitivity•Decision-MakingNets•DisplayStyleandPrinting•EquationstoGenerateTables•ReportsandDataLinking•CustomReports•Node-SetsandColoring•DynamicBayesNets•NetFragmentLibraries•TransformingaNet•ProcessCases•COMInterface–ProgrammingNetica•Bibliography•Netica-Web

InstallingNeticaonyourMac1.DownloadthetrialversionofCrossoverMac,andsaveittoyourharddrive.

HavingtroublefindingyourMacharddrive?SeeNavigatingFoldersbelow.2.AddtheCrossovericontoyourApplicationdirectory.IntheApplicationsdirectory,chooseNewFolderandnameit"Crossover".ThisiswhereyouwillsaveallWindows-basedprogramsmovingforward.3.DownloadtheNeticasoftwareapplication.YoumayobtainitbydownloadingfromtheNorsyswebsite,orotherwisefromNorsys.Double-clickthefileiconandextractittotheCrossoverfolderthatyoucreatedinStep2above.4.Double-clickontheNeticaicon ofNetica.exeinthedirectoryyouindicatedabove.5.Thereareafewminorbugswithright-clickingandonscreenhelp,formoreinformationseetheMacFAQpage.NavigatingFoldersinCrossoverMacDuetothenatureofrunningtwooperatingsystemsonyourmachine,thereareanumberofdrivesandfolderstonavigate,including(Z:),(Y:),(C:),(Desktop)and(MyComputer).Thus,itcanbeconfusingtonavigatethroughthefolderswhenyoufirstinstall,saveoropenNeticafilesonyourMac.HereisabreakdownofthevariousdrivesandfoldersunderCrossoverMac:1.Desktop:ThisisaWindowsreference.ThisisNOTyourMacdesktop.

Thereshouldbeaseparatefolderinthatsamelistofdirectoriescalled"MyMacDesktop".YouneedtoinstallNeticaonyourMacthroughthe(Z:)drive.Choose‘MyMacDesktop’ifyouwanttoaccessnon-applicationfilesonyourMac.2.MyComputer:Ifyouopen‘MyComputer’,youwillfind3drives:drive_c(C:)

/Users/yourcomputername(Y:)

/(Z:)–thisalsoshowsupasaniconofaharddrivewithablank(/)Drive_c:IfyouareusedtoworkingonaPC,theusualwaytosaveafileistheCdrive.ThisisnotthecasewhenyouareworkingwithCrossoverMac.TheCdrivehasafoldernamed"ProgramFiles".Donotbefooled,thesearenottheProgramFilesofyourMac!(Y:)takesyoudirectlytothemainaccountdirectoryofyourMac,whereyouwillseeafolderforyourDesktop,Downloads,Documents,etc./(Z:)isbasicallytheequivalenttothec:driveinWindows.ThepathtoyourMacApplicationsis:Z/Applications/CrossoverSaveNeticainthetopdirectoryoftheCrossoverfolder.Remember:YoucansaveyourBNfilesanywhereonyourMac.IfyouaretryingtoopenaBNfilefromsomewhereonyourMac,thepathtoyourDesktopis:Z/Users/YourUserName/Desktop.Orfrom“MyMacDesktop”.

Un-InstallingCrossover1.DropyourCrossOverbundleintothetrashandemptyit.ThismayfirstrequireyoutostoptheCrossOverCDHelper.Tostopitmanually,runtheActivityMonitor(usuallyfoundinyourApplications/Utilitiesfolder).SelectCrossOverCDHelperinActivityMonitorandclickQuitProcesstostopit.2.User-specificCrossOverfilesarelocatedinyourhomefolder,underthe:Library/ApplicationSupport/CrossOverhierarchy.TrashthatfolderanditscontentsforeachuserofCrossOveronyoursystem.3.Then,tobetrulycomprehensive,removethepreferencesfileslocatedin:Library/Preferences/calledcom.codeweavers.CrossOver.plist.4.IfyouhaveanypublishedbottlesorCrossOverhasbeenrunusingyoursystem'sadministratoraccount,youmayhavefilesin/Library/ApplicationSupport/CrossOveronyourstartupdrive.Thesemayalsobedeleted.

BuildingTablesfromOtherNetsTherearemanywaysthatNeticacanlearntheCPTsofnodes.Itlearnfromcasedata,learnfromacasefile,learnfromanExcelfileorlearnfromothernets(calledsourcenets).Inthelattercase,youwouldbebuildingadestinationnetthatrepresentsthesameworldasasourcenet.Inotherwords,NeticawilllearntheCPTtablesofasub-netwithinasourcenet.Alltheinferenceresultswillbethesameinbothnets.Thedifferenceisthatitisusingadifferentrepresentation,sothelinkstructurecanbedifferent.Inparticular,nodesthathavelinksinonenet,maynothavelinksintheotherandthelinkdirectionsmightbedifferent.

Howto:openanexistingnet,orcreateanewone.Ifitisanewnet,youmaywanttocopyandpastenodesfromthesourcenetintothedestinationnettoensurethenodeandstatenamesarethesame.Youcanthenselectasinglenode,ornonodes(inwhichcaseallnodeswillbelearned).NextchooseTable→BuildFromOtherNet.Neticawillautomaticallylearnthesub-setofCPTsfromthesourcenet.

Notes:

Nodesinthedestinationnetmusthavethesamenameandsamestatenamesasthesourcenet,buttheycanhavedifferenttitles.Youmaywanttocopy&pastenodesbetweennets(anddeletetheresultantinputlinks)toachievethis.

Neticacan'tlearnCPTsfromthesourcenetifthereisaparentnodeinthedestinationnetthatisnotinthesourcenet.Toresolvethis,firstlearnthetablesfromthesourcenet,thenaddthenewparent(s)tothedestinationnet.Thisisnottrueforchildrennodes.

Inbothcases,Neticawilllearnasmanyofthenodesaspossible.

Applications:whenyouarelearninganetfromdata,thelinkstructureusedcansignificantlyaffectthequalityoflearning.Forexample,ifyouhaveatargetnode,NeticacandetermineaveryeffectiveTANstructure.However,tocombinewithothersub-nets,youmaywantadifferentlinkstructure.

So,youcancreateanetwiththelinkstructureyouwantandthenbuildit's

CPTsusingthelearnednetasthesourcenet.

Noisy-OrDistribution (DMprob.dist.forequations)

Usage: NoisyOrDist(e,leak,b1,p1,...bn,pn)

Definition: P(e)=1–[(1-leak)producti=1ton(bi?(1-pi):1)]

Required: 0 leak 1e,biBoolean0 pi 1

Usethisdistributionwhenthereareseveralpossiblecausesforanevent,anyofwhichcancausetheeventbyitself,butonlywithacertainprobability.Also,theeventcanoccurspontaneously(withoutanyoftheknowncausesbeingtrue),withprobabilityleak(makethiszeroifitcan’toccurspontaneously).

Eachbiisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleanvariable,whichmaycausetheeventwhenitsTRUE.eisalsoaboolean,whichindicateswhethertheeventoccurs.EachofthepiaretheprobabilitythatewilloccurifbiisTRUEinisolation.

Ifleakiszero,andonlyonepossiblecauseisTRUE,saybk,thentheprobabilityforeispk.IfmorepossiblecausesareTRUE,P(e)willbegreater.Andifleakisnonzero,P(e)willbegreater.ReducingapialwaysresultsinthesameorlowerP(e).

picanbeconsideredthe“strength”oftherelationbetweeneandbi,withzeroindicatingindependence(linkcouldberemoved),and1indicatingmaximumeffect.

SeePearl88,page184formoreinformation(hisqi=1–pi).

Example: P(Effect|Cause1,Cause2)=

NoisyOrDist(Effect,0.1,Cause1,0.2,Cause2,0.4)

AnotherExample

SeealsoNoisyAndDist,NoisyMaxDist(fornodeswithmorethanjust2

states),NoisySumDist.

OtherSmallerImprovementsInadditiontoitsmajornewfeatures,Neticahasthefollowingimprovements.

Fromversion5.00toversion5.03

•Whenprintinganet,youcanenterthenumberofpagesyouwantittoappearon,insteadofjustthemagnification.Defaultis1.Butifyouwanttoenteramagnification,justmakethoseentriesblank.

•Keepstrackofstartingexperienceusedforlearning(normally1foreachstate).SavesinNETAfileforeachnode,andadjustswhendoingtablehardeningorsoftening.

•Fixed:WhenselectmultiplenodesanddoSensitivitytoFindings,gavea#2516error.

•Fixed:Sometimesconstantnodesweren'tregisteredtobeavailabletoequationsuntilaftersavingtofileandre-reading.

•WhileEMlearningfromacasefilehavingacaseinconsistentwiththeBayesnet,nowputstheIDnumofthecaseintheerrormessage,andallowshaltingorcontinuingwithoutit.

•Equationsnowrecognizediscreteconstantnodeswithastatesetting.•Namesofbuilt-innode-setsarenowprecededbycolon(:)insteadofdash(-)

•Fixed:Process-casesdidn'tworkwhentherewasafindingenteredinthenet(gavea2592C0000005error).

Fromversion4.00toversion4.16

•GreatlyimprovedtheCPTableeditor,bothcosmeticallyandfunctionally.•Texteditor:Handleslargertextfiles(upto2GB)fortextediting,insteadofjust30K.HelpsavoidMessagesWindowoverflow.Textentryindialogboxes(suchasuserfields)canalsotakelargertextamounts.

•Disconnecting/connectinglinksnowworksbetter.Thetoolbuttoncanreconnectaswellasdisconnect.Whenright-clickonadisconnectedlink,menunowhas"Reconnect",whichreconnectslinktooriginalnode(evenacrossfilesave/read).

•Cannowread.xlsxand.accdbdatabasecasefiles(aswellastheold.xlsand.mdb).

•Whenreadingacasefile,missingdatasymbols(empty,'',?,*,N/A)willnowinsteadbeinterpretedasastate,ifthenodehasastatewithanexactlymatchingstatetitle.

•Newonscreenhelpsystem.•Within.dnefiles,itnowusesasuperiorflatformatfortables(whichmeanstheBayesnetfilesitcreatescannotbecompletelyreadbyveryoldversionsofNetica(previousto2.27of2003-05-02)).But,ofcourse,newversionsofNeticacanstillreadalltheold.dnefiles,createdbyanypreviousversionofNetica.

•Fixed:WhenreadingUVFfiles,uncertainfindingsforstateswithan_intheirnamecausederror#2878.

•Fixed:WhenreadingUVFfiles,extraspacescouldcauseerrors.•Fixed:WhenleftandrightmousebuttonsinWindowswereconfiguredasleft-handed,Neticacouldn'tselectnodes.

•Fixed:ReadingHuginfilesdidn'tworkaswellasearlierversionsofNetica.•CannowreadXMLBIF0.3files,asdescribedin1998FabioCozmandocument:http://www.cs.cmu.edu/afs/cs/user/fgcozman/www/Research/InterchangeFormat/

•Mousewheelnowscrollsinsteadofzooms.•Nodedialog:Fixedupthenodepropertiesdialogboxmultipurposeboxdisplayandentryofstateinfo(statenames,statetitles,statecomments,statenumbers)significantly(eg,allowsingleentryor"All"atonceforeach).

Fromversion3.18toversion3.25:

•Fixedbug:Sometimesafteraddingautilitynode(oranyundiscretizedcontinuousnode),andthentryingtoaccessitstable,aninternalerrorwouldresult.•ImprovedUnicodesupport(LabelBoxdisplay,docnnodes,settingbyright-clicking,etc.)•Fixed"ProcessCases"toworkwithUVFfiles.•Undo/redofornodesetoperationsnowworksproperly.

•Obfuscatenetdeletesdocumentationnodes.•ImprovedthesupportforoldversionsofMicrosoftWindows(Windows95,98,Me).

Fromversion3.16toversion3.18:

•Tableeditornowhasa*indicatorinitstitlebartoshowwhenchangeshavebeenmadethatarenotyetappliedtothenode.•Commentsthatyoucreatetoappearwhenthemousehoversoveranodeorstatecannowbemulti-line.•Linksarenowalwaysdrawnunderneaththenodesfordiagramclarity.•Fixedannoyingsituationwhereequationisconstantlyre-establishedwhentryingtodeleteequationfromnodepropertiesdialogbybackspacing.•Fixedproblemsoccurringwhennodefaultprinterisinstalled,suchaserrormessage:**1223**Xcomponentof`drawingbounds`inVISUALnet'V1'istoolarge(=...,butmaximumis16383).•Fixedbug:Databaseaccessgaveanerrorwhenthefirstnodeinthenetwasskipped(i.e.,wasn'tadatabasecolumn).•Lotsofsmallimprovementstothetableeditordialogbox.•Fixedbug:'AddCaseFileNodes'didn'tdoanythinginsomesituations.•Cannowscrollwitharrowkeys.•Cannowenteremptystringsforvaluesofuser-definedfieldsinnodedialogbox.•Ifnodesateachendofalinkarein"hidden"format,thelinkisnotdrawn.•Otherminorimprovementsandbugfixes.

DoingProbabilisticInferenceAfteraBayesnethasbeenconstructedandcompiled,youcanapplyittoaparticular=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_case.htm');returnfalse;">casebyenteringfindings(alsoknownas“evidence”),whicharethevaluesfornodesthatyouknow.Thenyouusebeliefupdating(whichisaformofprobabilisticinference)todeterminenewprobabilitiesforthestatesofalltheothernodes.

Youcanrunthroughtheprocessusingthisexample.

Aswellasfindingbeliefs,Neticacanfindthemostlikelyconfigurationoftheremainingvariables,accordingtothefindingsentered.Thisiscalledthe“MostProbableExplanation”.

YoucanalsouseNeticatodosensitivityanalysistofindhowtightlycouplednodesare.Thatcanbeusedtodeterminethedegreetowhicha=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingatonenodeisexpectedtochangethebeliefsatothernodes,orwhichnodeswouldbethebesttoobtainfindingsfor,inordertoobtainmaximuminformationonanothernode.

ProbabilisticInferencebyNodeAbsorptionItispossibletodo=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_probabilistic_inference.htm');returnfalse;">probabilisticinferenceusingnodeabsorption,by=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_enter_finding.htm');returnfalse;">enteringallthefindings,andthenabsorbingallthenodesexceptforasinglequerynode.Theresultingprobability=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_CPT.htm');returnfalse;">CPTforthatnodewillbeasinglebeliefvector(becausethenodewon’thaveanyparents),whichisthesameasthebeliefsthatwouldbeobtainedbycompilingtheBayesnetanddoingbeliefupdating.Ofcourse,thenetisdestroyedintheprocess,butyoucanrecoveritbychoosingEdit→Undo.Normallyitisbettertodoinferenceby=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_compile_net.htm');returnfalse;">compilingthenetanddoing=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_belief_updating.htm');returnfalse;">beliefupdating,butsometimesadditionalinsightsaregainedbyusingnodeabsorptionforinference.

Itshouldbementionedthatnodeabsorptionwillalsoworkwith=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_decision_nets.htm');returnfalse;">decisionnets.Tosolveadecisionnet,selectallitsnodes,andclickthe toolbutton.Thenaturenodeswillallbeabsorbedout.Whenadecisionnodeisabsorbed,itisnotremovedfromthenet;insteaditiscompletelydisconnectedanditsdecisiontablesettotheoptimaldecisionfunction.Utilitynodesarealsoleft,soyoucanseetheexpectedutility.ThealgorithmusedisdescribedinShachter86,Shachter88andShachter89.

Whenusingnodeabsorptiontosolvedecisionproblems,thedecisionnodes

musthave=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_no_forgetting_link.htm');returnfalse;">no-forgettinglinks.Theremustbeonlyoneutilitynode,withnodescendants.Andifnotallthenodesofthenetarebeingabsorbed,theymustconsistofadescendantsubnet.So,ifnodesareabsorbedone-by-one,asuitableordermustbeused.TheserestrictionsareexplainedinmoredetailintheShachterreferencesmentionedabove.Ifanyoftheserestrictionsarenotmet,Neticawillnotproduceanerroneousresult,butwilljustabsorbasmanyofthenodesasitcan,andthendisplayamessageexplainingwhyitwasimpossibletoproceed.

rect (functionforequations)

Usage: rect(x,a,b)

Definition: (a<=x&&x<b)?1:0

Required: a b

Returns1ifxisbetweenaandb,otherwise0.

Thisfunctionisoftenmultipliedbyanotherto"captureapiece"oftheotherfunction.

Alsoknownasthe"rectangularfunction"becauseoftherectangularshapeofitsgraph.

ThisfunctionisthesameastheprobabilitydistributionUniformDist,exceptheightofUniformDisttheisnormalizedsothattheareaunderitscurveis1.

Ifbisinfinity,the"unitstepfunction"isformed.

Seealsoclip,andsign.

Inordertodosomeoperationsonanode,youfirstselectitbyclickingonceonit,anditwillthenbedrawnusingnegativecolorstohiliteit.Youcanselectseveralnodesatatimebyclickingonthebackgroundanddraggingtheselectionrectangletoincludethem.Toaddorremovenodesfromyourselection,holddowntheCTRLkeywhileyoudotheselectionoperation,orright-clickonthenodeandchooseSelect/Deselect.MoreInfo

BetaDistribution (continuousprobabilitydistforequations)

Usage: BetaDist(x, , )

Definition: x^( -1)(1-x)^( -1)/beta( , )

wherebetaisthebetafunction

Required: >0 >0

Support: 0 x 1

Moments: = /( + )

^2= /[( + )^2( + +1)]

1=2( – )sqrt(( + +1)/( ))/( + +2)

2=3( + +1)[2( + )^2+ ( + -6)]/[ ( + +2)( + +3)]

Almostanyreasonablysmoothunimodaldistributionon[0,1]canapproximatedbysomebetadistribution(ifitsnoton[0,1],seeBeta4Dist).AnimportantuseofthebetadistributionisasaconjugatedistributionfortheparameterofaBernoullidistribution.

HiddenNodeStyleSometimesitisusefultohidenodesinyournet,especiallywhenworkingwithlargenets.

Tounhideanode(s):

1.Clickdownonthenetbackground(i.e.notonanodeorlink),andthendragwiththemousesothatthedashedlinerectanglegoesoverthenodethatwasmadehidden.Thenodewillthenbeselected(eventhoughyoucan'tseeit),soyoucanchooseStyle→Defaultfromthemenuto"bringitback"(availablefromboththeoverheadandright-clickmenus).

2.Alternately,ifitwon'tharmanyothernodes,youcanjustdoCTRL-Atoselectallthenodes,thenchooseStyle→Defaultfromthemenu.

3.Ifhidingthenodewasthelastactionyouperformed,youcansimplyclicktheUndoarrowordoCTRL-Z.

NormalDistribution (continuousprobabdistforequations)

Usage: NormalDist(x, , )

Definition: [1/( sqrt(2 ))]exp(-[(x- )/ ]^2/2)

Required: >0

Support - x

Moments: mean=

standarddeviation=

1=0 2=3

Thenormaldistribution,orapproximationsofit,arisefrequentlyinnature(thisispartlyexplainedbythe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_central_limit_theorem.htm');returnfalse;">centrallimittheorem).Sinceitalsohasmanyconvenientmathematicalpropertiesitisthemostcommonlyusedcontinuousdistribution.

Forthisdistribution,68.2%oftheprobabilityiswithin1standarddeviationofthemean,95.4%iswithin2standarddeviations,and99.74%iswithin3standarddeviations.

If =0, =1itisknownasa“standardnormal”distribution.

_find0FunctionThisisafunctionthatNeticausesinternallytofindthestateofadiscretenodehavingnumericvaluesassociatedwithitsstates,givenoneofthosenumericvalues.IfNeticagivesyouamessagesayingtherewasanerrorevaluating_find0(z,x0,x1,...xn),wherethezandxiarenumbers,thenyourequationissupplyingillegalvalues,evenifyouneverexplicitlyused_find0inyourequation.

Thevalueofzmustequaloneofthexi,orelsetheequationissayingthatthenodehasavaluethatisnotrepresentedbyanyofitsstates.Youcanchangetheequationtoonlysupplynumbersthatmatchthoseattachedtothestateofthenode(perhapsusingnearest),oryoucanchangethenumbersattachedtothestates.Or,ifyouwishittobeabletomatchnumbersinbetweenthexi,thenyoushouldchangethenodetoacontinuousone,andleavethesamesetofattachednumericvaluesasitsdiscretizationthresholds.

_BernoulliFunctionThisisadistributionthatNeticausesinternallytorepresenttheBernoullidistribution.Ifyougetanerrormessagesayingtherewasanerrorevaluating_Bernoulli(k,p),wherekandparenumbers,thenyourequationissupplyingillegalvalues,evenifyouneverexplicitlyused_Bernoulliinyourequation.

Forinstance,ifyourequationfor=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleannodeBisP(B|x)=x/10andvaluesofxcangoupto11,then_Bernoulli(1,1.1)willbeillegal,sinceyouaresupplying1.1asaprobability(andNeticacan’tnormalizeit,sincenoprobabilityforBbeingfalseisgiven).

round (functionforequations)

Usage: round(x)

Definition: floor(x+1/2)

Required: xisanunrestrictedreal

Roundsxtothenearestinteger.Toroundofftootherquantities,useroundto.

roundto (functionforequations)

Usage: roundto(dx,x)

Definition: dx*floor((x+dx/2)/dx)

Required: dx>0

Roundsxtothenearestdx,whichmaybelessthanorgreaterthan1.

Forexample,roundto(10,17)rounds17tothenearest10,andsoitreturns20.

Ifdx=1,thenthisisthesameasround.

approx_eq (functionforequations)

Usage: approx_eq(x,y)x~=y

Definition: eqnear(2e-5,x,y)Definitionofeqnear

Required: xandyareunrestrictedreals

Returnstrueiffxisequaltoy,withinasmallrelativetolerance.

Usuallytheoperatorformofthisfunctionismostconvenient:x~=y

Tohavecontrolofthetolerance,useeqnear.

eqnear (functionforequations)

Usage: eqnear(reldiff,x,y)

Definition: |X-Y|/max(|X|,|Y|)<=reldiff

Required: reldiff>=0

Returnstrueiffxisequaltoy,withinreldiff.

TohaveNeticachoosereldiff,useapprox_eq.

clip (functionforequations)

Usage: clip(min,max,x)

Definition: (x<min)?min:(x>max)?max:x

Required: min max

Returnsx,unlessitislessthanmin(inwhichcaseitreturnsmin),ormorethanmax(inwhichcaseitreturnsmax).

Seealsomax,min,andrect.

sign (functionforequations)

Usage: sign(x)

Definition: (x>0)?1:(x<0)?-1:0

Required: xisanunrestrictedreal

Returns1ifxispositive,-1ifxisnegative,and0ifxiszero.

Seealsorect,clip,andabs.

xor (functionforequations)

Usage: xor(b1,b2,...bn)

Definition: odd(NumberTrue(b1,b2,...bn))

Required: biareboolean

Returnstheexclusive-orofb1,b2…bn.

Thisisalsoknownastheparityfunction,andwillreturntrueiffanoddnumberofbievaluatetotrue.

Seealsoand,or,not,andequal.

increasing (functionforequations)

Usage: increasing(x1,x2,...xn)

Definition: (x2>x1)&&(x3>x2)&&...&&(xn>xn-1)

Required: xiareunrestrictedreals

Returnstrueiffeachxiisgreaterthanthepreviousone.

Ifyouwishthetesttobe“greaterthanorequals”,useincreasing_eq.

Seealsogreater.

increasing_eq (functionforequations)

Usage: increasing_eq(x1,x2,...xn)

Definition: (x2>=x1)&&(x3>=x2)&&...&&(xn>=xn-1)

Required: xiareunrestrictedreals

Returnstrueiffeachxiisgreaterorequaltothepreviousone.

Ifyouwishittobejustgreaterthan,useincreasing.

Seealsogreater_eq.

avg (functionforequations)

Usage: avg(x1,x2,...xn)

Definition: (x1+x2+...+xn)/n

Required: xiareunrestrictedreals

Returnstheaverage(i.e.mean)ofx1,x2,…xn.

Atleastoneargumentmustbepassed.

Seealsomax.

Example: min(10,6.6,3.4,126,3.4)returns3.4

mag (functionforequations)

Usage: mag(x1,x2,...xn)

Definition: sqrt(x1^2+x2^2+...+xn^2)

Required: xiareunrestrictedreals

Returnsthemagnitudeofthevector[x1,x2,…xn].ThisisalsoknownastheEuclideanlengthofthevector.

Iftherealandimaginarypartofacomplexnumberarepassed,themagnitudeofthecomplexnumberisreturned.

Ifnoargumentsarepassed,zeroisreturned.Ifoneargumentispassed,itsabsolutevalueisreturned.

Seealsoabs,max.

Example: mag(1.5,0,-2)returns2.5

min (functionforequations)

Usage: min(x1,x2,...xn)

Definition: xis.t.(xi<=xj)forallj

Required: xiareunrestrictedreals

Returnstheminimumofx1,x2,…xn.

Atleastoneargumentmustbepassed.

Ifyoujustwanttheindexoftheminimum(i.e.itspositioninthelist),useargmin.

Seealsomax.

Example: min(10,6.6,3.4,126,3.4)returns3.4

max (functionforequations)

Usage: max(x1,x2,...xn)

Definition: xis.t.(xi>=xj)forallj

Required: xiareunrestrictedreals

Returnsthemaximumofx1,x2,…xn.

Atleastoneargumentmustbepassed.

Ifyoujustwanttheindexofthemaximum(i.e.itspositioninthelist),useargmax.

Seealsomin.

Example: max(-10,6.6,3.4,-126,3.4)returns6.6

argmin (functionforequations)

Usage: argmin0(x0,x1,...xn)

argmin1(x1,x2,...xn)

Definition: is.t.(xi<=xj)forallj

Required: xiareunrestrictedreals

Returnstheindex(positioninlist)oftheargumentwiththelowestvalue.Ifthereareseveralwiththesamelowestvalue,thentheindexofthefirstoccurrencewillbereturned.Thefirstargumenthasindex0ifargmin0isused,orindex1ifargmin1isused.

Atleastoneargumentmustbepassed.

Ifyouwanttheminimumvalueitself,ratherthanitsindex,insteadusemin.

Seealsoargmax.

Examples: argmin0(10,6.6,3.4,126,3.4)returns2

argmin1(-5e3,6.6,3.4,-126)returns1

argmax (functionforequations)

Usage: argmax0(x0,x1,...xn)

argmax1(x1,x2,...xn)

Definition: is.t.(xi>=xj)forallj

Required: xiareunrestrictedreals

Returnstheindex(positioninlist)oftheargumentwiththehighestvalue.Ifthereareseveralwiththesamehighestvalue,thentheindexofthefirstoccurrencewillbereturned.Thefirstargumenthasindex0ifargmax0isused,orindex1ifargmax1isused.

Atleastoneargumentmustbepassed.

Ifyouwanttheminimumvalueitself,ratherthanitsindex,insteadusemax.

Seealsoargmin.

Examples: argmax0(1,-6.6,3.4,1.26,3.4)returns2

argmax1(5e3,-6.6,-3.4,126)returns1

nearest (functionforequations)

Usage: nearest0(val,x0,x1,...xn)

nearest1(val,x1,x2,...xn)

Definition: is.t.(|val-xi|<=|val-xj|)forallj

Required: valandxiareunrestrictedreals

Returnstheindex(positioninlist)oftheargumentwiththevalueclosesttoval(asmeasuredbytheabsolutevalueofthedifference).Ifthereareseveralwiththesamesmallestdifference,thentheindexofthefirstoccurrencewillbereturned.Thefirstxargumenthasindex0ifnearest0isused,orindex1ifnearest1isused.

Mustbepassedatleast2arguments(valandanx).

Fortheinversefunction,seeselect.

Seealsomember.

Examples: nearest0(1,1,3.4,1,3.4)returns0

nearest1(5e3,-6.6,-3.4,126)returns3

select (functionforequations)

Usage: select0(index,x0,x1,...xn)

select1(index,x1,x2,...xn)

Definition: xis.t.i==index

Required: indexisinteger,xiareallthesametypeselect0:0 index<n

select1:0<index n

Returnsthevalueofthexargumentatpositionindex:x[index]

Thefirstxargumentisatindex0ifselect0isused,andatindex1ifselect1isused.

Mustbepassedatleast2arguments(indexandanx).

Fortheinversefunction,seenearest.

Examples: select0(1,-6.6,3.4,1.26,3.4)returns3.4

select1(1,-6.6,3.4,1.26)returns–6.6

member (functionforequations)

Usage: member(elem,s1,s2,...sn)

Definition: (elem==s1)||(elem==s2)||...||(elem==sn)

Required: elemandallsimustbethesametype

Returnstrueiffoneofthesiargumentshasthesamevalueaselem..

Seealsonearest.

Examples: member(1,-6,3,1,3)returnstrue

member(C,blue,red)andC=redreturnstrue

factorial (functionforequations)

Usage: factorial(n)

Definition: n(n–1)(n–2)...1

Required: n 0nisaninteger

Returnsthefactorialofn,whichistheproductofthefirstnintegers.

factorial(n)isoftenwrittenasn!

factorial(0)=1

Evenfairlysmallvaluesofn(around170)cancausefactorialtooverflow.Forthatreasoncalculationswiththefactorialfunctionareoftendoneusingthelogarithmoftheresults,forwhichyoucanuselogfactorial.

Ifnisnotanintegeryoumaywanttousethegammafunction,whichforintegervaluesisrelatedtofactorialby:factorial(n)=gamma(n+1)butwhichisalsodefinedfornon-integervalues.

logfactorial (functionforequations)

Usage: logfactorial(n)

Definition: log(n(n–1)(n–2)...1)

Required: n 0nisaninteger

Returnsthenaturallogarithmofthefactorialofn(i.e.n!).

Ifnisnotanintegeryoumaywanttousetheloggammafunction,whichforintegervaluesisrelatedtologfactorialby:logfactorial(n)=loggamma(n+1)butwhichisalsodefinedfornon-integervalues.

logistic (functionforequations)

Usage: logistic(t)

Definition: exp(t)/(1+exp(t))

Required: tisanunrestrictedreal

Logisticisalsoknownas"expit",or"sigmoid".

Thisistheinverseofthelogitfunction(alsoknownaslogodds).

SeealsoLogisticDist,logit.

Example: expit(0)returns0.5expit(1)returns0.7310585

logit (functionforequations)

Usage: logit(p)

Definition: log(p/(1-p))

Required: 0<p<1

logitisalsoknownas"logodds".

Thisistheinverseofthelogisticfunction(alsoknownas"expit"or"sigmoid")

Itapproachesnegativeinfinityaspapproaches0,andpositiveinfinityaspapproaches1.

Seealsologistic.

Example: logit(0.5)returns0logit(0.75)returns1.0986123

gamma (functionforequations)

Usage: gamma(x)

Required: x 0

Returnsthegammafunctionofx.

Thegammafunctionisnormallydefinedfornegativevaluesofxaswell,butNeticacannotcomputethese.

Don’tconfusethisfunctionwiththegammaprobabilitydistribution.

Evenfairlysmallvaluesofx(around170)cancausegammatooverflow.Forthatreasoncalculationswiththegammafunctionareoftendoneusingthelogarithmoftheresults,forwhichyoucanuseloggamma.

Forintegervaluesofx,thegammafunctionisrelatedtothefactorialfunctionby:factorial(n)=gamma(n+1)

loggamma (functionforequations)

Usage: loggamma(x)

Definition: log(gamma(x))

Required: x 0

Returnsthenaturallogarithmofthegammafunctionofx.

Theloggammafunctionisnormallydefinedfornegativevaluesofxaswell,butNeticacannotcomputethese.

beta (functionforequations)

Usage: beta(z,w)

Definition: gamma(z)gamma(w)/gamma(z+w)

Required: z>0w>0

Returnsthebetafunctionofzandw.

BetaDististhebetaprobabilitydistribution,whichisbasedonthebetafunction.

Seealsogamma.

erf (functionforequations)

Usage: erf(x)

Definition: (2/sqrt( ))Integralfrom0toxofexp(-t^2)dt

Required: xisanunrestrictedreal

Thisreturnstheerrorfunctionofx.Itisusefulforcalculatingintegralsofthenormaldistribution.

Ifxislarge,youcanobtainbetteraccuracywitherfc.

erfc (functionforequations)

Usage: erfc(x)

Definition: 1–erf(x)(definitionoferf)

Required: xisanunrestrictedreal

Thisreturnsthecomplementaryerrorfunctionofx.Itisusefulforcalculatinganintegralofatailofanormaldistribution.

Itwouldbeeasyenoughtojustuse1-erf(x),butthisprovidesbetternumericalaccuracywhenxislarge(soerf(x)isverycloseto1).

binomial (functionforequations)

Usage: binomial(n,k)

Definition: n!/(k!*(n-k)!)

Required: 0 k nnandkareintegers

Returnsthebinomialcoefficient(nk).Thisisthenumberofdifferentk-sizedgroupsthatcanbedrawnfromasetofndistinctelements.Seealsothemultinomialfunction.

BinomialDististhebinomialprobabilitydistribution,whichisbasedonthebinomialcoefficient.

multinomial (functionforequations)

Usage: multinomial(n1,n2,...nn)

Definition: (n1+n2+...nn)!/(n1!*n2!*...nn!)

Required: ni 0niareintegers

Returnsthenumberofwaysan(n1+n2+…nn)sizedsetofdistinctelementscanbepartitionedintosetsofsizen1,n2,…nn.Ifpartitioningintoonlytwosets,thisisthesameasbinomial.

Theprobabilitydistributionbasedonthisfunctionisthemultinomialdistribution.

UniformDistribution (continuousprobabilitydistforequations)

Usage: UniformDist(x,a,b)

Definition: 1/(b-a)

Required: b>a

Support: a x b

Moments: =(a+b)/2 =(b-a)/sqrt(12)

1=0 2=1.8

Thisisthedistributiontousewhentheminimumandmaximumpossiblevaluesforavariableareknown,butwithinthatrangethereisnoknowledgeofwhichvalueismorelikelythananother.

Ithasaconstantvaluefromx=atox=b,andzerovalueoutsidethisrange.

Alsoknownasthe"rectangulardistribution",andsimilartotherectfunction.

TriangularDistribution (continuousprobabdistforequations)

Usage: TriangularDist(x,m,w)

Definition: (w-|x-m|)/w^2

Required: w>0

Support: m-w x m+w

Moments: =m =w/sqrt(6)

1=0 2=2.4

Thegraphofthisdistributionhasatriangularshape,withthehighestpointatx=a,andnonzerovaluesfroma-wtoa+w.

SeealsoTriangular3Dist,andTriangularEnd3Dist.

AsymmetricTriangularDistribution (continuousprob.dist.forequations)

Usage: Triangular3Dist(x,m,w1,w2)

Definition: 2(x-m+w1)/(w1(w1+w2))form-w1<=x<=m,

2(m+w2-x)/(w2(w1+w2))form<=x<=m+w2

Required: w1 0w2 0w1&w2can'tbothbe0

Support: m-w1 x m+w2

Moments: m w2–w1 3

The=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_pdf.htm');returnfalse;">pdfhasatriangularshape,withthehighestpointatx=m,andnonzerovaluefromm-w1tom+w2.

SeealsoTriangularDist,andTriangularEnd3Dist.

AsymmetricTriangularRangeDistribution (cpdistforequations)

Usage: TriangularEnd3Dist(x,m,a,b)

Definition: 2(x-a)/((b-a)(m-a))fora<=x<=m,

2(b-x)/((b-a)(b-m))form<=x<=b

Required: a m ba b

Support: a x b

Moments: a+b+m /3

^2 a^2+b^2+m^2-ab-am-bm /18

The=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_pdf.htm');returnfalse;">pdfhasatriangularshape,withthehighestpointatx=m,andnonzerovaluefromatob.

SeealsoTriangular3Dist,andTriangularDist.

LognormalDistribution (continuousprobabilitydist.forequations)

Usage: LognormalDist(x, , )

Definition: N(log(x), , )/x

=(1/[x sqrt(2 )])exp(-[(log(x)- )/ ]^2/2)

whereNisthenormaldistribution

Required: >0

Support: x>0

Moments: =exp( + ^2/2)

^2=exp(2 + ^2)[exp( ^2)–1]

1=[exp( ^2)+2]sqrt(exp( ^2)–1)

2=exp(4 ^2)+2exp(3 ^2)+3exp(2 ^2)

Thelognormaldistributionresultswhenthelogarithmoftherandomvariableisdescribedbyanormaldistribution.Thisisoftenthecaseforavariablewhichistheproductofanumberofrandomvariables(bythe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_central_limit_theorem.htm');returnfalse;">centrallimittheorem).

Noticethatthe‘n’ofLognormalisnotcapitalized,indicatingthatthisisnotthesameasthelogarithmofthenormaldistribution.

ExponentialDistribution (continuousprobabilitydistforequations)

Usage: ExponentialDist(x, )

Definition: exp(- x)

Required: >0

Support: x 0

Moments: =1/ =1/

1=2 2=9

Ifeventsoccurbya=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Poisson_process.htm');returnfalse;">Poissonprocess,thenthetimebetweensuccessiveeventsisdescribedbytheexponentialdistribution(where istheaveragenumberofeventsperunittime).

GammaDistribution (continuousprobabilitydistforequations)

Usage: GammaDist(x, , )

Definition: x^( -1)exp(-x/ )/(gamma( ) ^ )

=exp[( -1)log(x)-x/ -log(gamma( ))- log( )]

Parameters: isshape isscale

Required: >0 >0

Support: x 0

Moments: = = sqrt( )

1=2/sqrt( ) 2=3+6/

Ifeventsoccurbya=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Poisson_process.htm');returnfalse;">Poissonprocess,thenthetimerequiredfortheoccurrenceof eventsisdescribedbythegammadistribution(where istheaveragetimebetweenevents).

For =1,thisistheexponentialdistributionwith =1/ .For =2,thisisthechi-squaredistributionwithdegreesoffreedom =2 .

TheErlangdistributionisaspecialcaseofthegammadistributioninwhich=1and =n(whichisaninteger).

WeibullDistribution (continuousprobabilitydistforequations)

Usage: WeibullDist(x, , )

Definition: ( / )(x/ )^( -1)exp(-(x/ )^ )

Parameters: isshape isscale

Required: >0 0

Support: x 0

Moments: = gamma(1+1/ )

^2= ^2[gamma(1+2/ ) gamma(1+1/ )^2]

1=[gamma(1+3/ )-3gamma(1+1/ )gamma(1+2/ )+2gamma

(1+1/ )^3]/[gamma(1+2/ )–gamma(1+1/ )^2]^(3/2)

2=[gamma(1+4/ )-4gamma(1+1/ )gamma(1+3/ )+6gamma

(1+1/ )^2gamma(1+2/ )-3gamma(1+1/ )^4]/[gamma(1+2/ )-gamma(1+1/ )^2]^2

TheWeibulldistributionisoftenusedforreliabilitymodels,sinceifthefailurerateofanitem(i.e.,percentoftheremainingoneswhichfail,asafunctionoftime)isgivenas:Z(t)=rt^( -1),thenthedistributionofitemlifetimesisgivenbytheWeibulldistributionwithr= / ^ .

GeneralizedBetaDistribution (contprob.distforequations)

Usage: Beta4Dist(x,a,b,c,d)

Definition: Be((x-c)/(d-c), , )

whereBeisthebetadistribution

Parameters: cislowerendpointdisupperendpoint

Required: >0 >0d>c

c x d

Thisisabetadistributionthathasbeenshiftedandscaled,sothatthe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_pdf.htm');returnfalse;">pdfhasnonzerovaluesfromx=ctox=d,insteadoffromx=0tox=1.Thisdistributionhasgreatflexibilitytofitalmostanysmooth,unimodaldistributionwithnotails(i.e.,onlynonzerooverafiniterange).

CauchyDistribution (continuousprobabdistforequations)

Usage: CauchyDist(x, , )

Definition: 1/( (1+((x- )/ )^2))

Parameters: =location =scale

Required: >0

Moments: =undefined =undefined

Althoughreal-worlddatararelyfollowsaCauchydistribution,itisusefulbecauseofitsunusualness.Forexample,althoughitissymmetricabout(whichisthereforeitsmedianandmode),itdoesn'thaveamean(orvariance,etc.)becausetheappropriateintegralsdon'tconverge.TheC(0,1)distributionisalsoStudent'stdistributionwithdegreesoffreedom=1.

LaplaceDistribution (continuousprobabilitydistforequations)

Usage: LaplaceDist(x, ,

Definition: (1/(2 ))exp(-|x- |/ )

Required: b>0

Support: - x

Moments: mean

^2 2 ^2

1=0 2=3

Its=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_pdf.htm');returnfalse;">pdfistwoexponentialdistributionssplicedtogetherback-to-back.ThedifferencebetweentwoiidexponentialdistributionrandomvariablesfollowsaLaplacedistribution.

Alsoknownasthe"doubleexponential"distribution.

ExtremeValueDistribution (continuousprobab.dist.forequations)

Usage: ExtremeValueDist(x, , )

Definition: exp(-exp(-(x- )/ )-(x- )/ )/

Parameters: =location =scale

Required: >0

Moments: = + ( =Eulers=0.5772156649)

= /sqrt(6)

1=1.3 2=5.4

Thisdistributionisthelimitingdistributionforthesmallestorlargestvaluesinlargesamplesdrawnfromavarietyofdistributions,includingthenormaldistribution.

Alsoknownasthe"Fisher-Tippetdistribution","Fisher-TippetTypeIdistribution"orthe"log-Weibulldistribution".

ParetoDistribution (continuousprobabdistforequations)

Usage: ParetoDist(x,a,b)

Definition: (a/b)(b/x)^(a+1)

Parameters: aisshapebislocation

Required: a>0b>0

Support: x b

Moments: =ab/(a-1)fora>1( fora 1)

^2=ab^2/[(a-1)^2(a-2)]fora>2

( if1<a 2,non-existentifa 1)

1=[2(1+a)/(a-3)]sqrt((a-2)/a)fora>3

2=6(a^3+a^2–6a-2)/[a(a-3)(k-4)]fora>4

TheParetodistributionisapowerlawprobabilitydistributionfoundinalargenumberofreal-worldsituations,suchasthedistributionofwealthamongindividuals,frequenciesofwords,sizeofparticles,sizeoftowns/cities,areasburntinforestfires,sizeofsomefractalfeaturesetc.Thesearesituationswheretherearemanythataresmallandafewthatarelarge(liketheParetoprinciple,inwhich20%ofthepopulationowns80%ofthewealth).

Foranyvalueofa,thedistributionis"scale-free",whichmeansthatnomatterwhatrangeofxonelooksat,theproportionofsmalltolargeeventsisthesame(i.e.,theslopeofthecurveonanysectionofthelog-logplotisthesame).

AlsoknownastheBradforddistribution.

Chi-SquareDistribution (continuousprobabilitydistforequations)

Usage: ChiSquareDist(x,n)

Definition: x^( /2-1)/[exp(x/2)2^( /2)gamma( /2)]

Required: >0 isaninteger

Support: x 0

Moments: = ^2=2

1=2sqrt(2/ ) 2=3+12/

ThisisthedistributionofZ1^2+Z2^2+...Z ^2whereZiareindependentstandardnormalvariates.

isusuallycalledthe“degreesoffreedom”ofthedistribution.

Student'st-Distribution (continuousprobabilitydistforequations)

Usage: StudentTDist(x,

Definition: (( +1)/2)/[sqrt( pi)( /2)(1+x^2/ )^(( +1)/2)

Required: >0

Support: - x

Moments: m=0

^ for >2

1=0for >3 2=6/( -4)for >4

Thet-distributionorStudent'st-distributionarisesintheproblemofestimatingthemeanofanormallydistributedpopulationwhenthesamplesizeissmall.

F-Distribution (continuousprobabilitydistforequations)

Usage: FDist(x, 1, 2)

Definition: [( 1x/( 2+ 1x))^(1/2)][( 2/( 2+ 1x))^( 2/2)]/[xbeta( 1/2, 2/2)]

wherebetaisthebetafunction

Required: >0 2>0

Support: x 0

Moments: 2/( 2-2)for >2

^ 2 2^2( 1+ 2-2)/[ 1( 2-2)^2( 2-4)]for 2>4

Theratiooftwochi-squaredvariatesX1andX2,eachdividedbytheirdegreesoffreedom:(X1/ 1)/(X2/ 2)followsanF-distribution.

SinglePointDistribution (discreteprobabilitydistforequations)

Usage: SingleDist(k,c)

Definition: (k==c)?1:0

Required:kandcareintegers

Support: k c

Moments: =c =01=undefined 2=undefined

Thesinglepointdistributionindicatesthatk=c.Theprobabilitythatkisanyothervalueis0.

Thisisthediscreteversionofadiracdelta.

DiscreteUniformDistribution (probabilitydistforequations)

Usage: DiscUniformDist(k,a,b)

Definition: 1/(b-a+1)

Required: b ak,a,bareintegers

Support: a k b

Moments: =(a+b)/2^2=(b-a)(b–a+2)/121=02=(3/5)[3–4/[(b-a)(b–a+2)]]

Thisdistributionrepresentsthesituationwherekhasanequalprobabilityoftakingonanyoftheintegervaluesfromatobinclusive(whereaandbareintegers).Ifkwerecontinuous,thenitwouldbeacontinuousuniformdistribution.

BernoulliDistribution (discreteprobabilitydistforequations)

Usage: BernoulliDist(b,p)

Definition: b?p:1-p

Required: 0 p 1bboolean

Moments: =p^2=p(1–p)1=(1-2p)/sqrt(p(1-p))2=3+[1-6p(1-p)]/[p(1-p)]

Thisisthedistributionforasingle"Bernoullitrial",inwhichpistheprobabilityofanoutcomelabeled"success"occurring.bisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleanthatistrueifthe"success"occurs.Anexampleisflippingacoinandcheckingfortheeventofheadsappearing.

BinomialDistribution (discreteprobabilitydist.forequations)

Usage: BinomialDist(k,n,p)

Definition: binomial(n,k)p^k(1-p)^(n-k)Definitionof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_binomial_coefficient.htm');returnfalse;">binomial

Required: 0 p 1kandnareintegers

Support: 0 k n

Moments: =np^2=np(1–p)1=(1-2p)/sqrt(np(1-p)2=3+[1-6p(1-p)]/[np(1-p)]

A=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bernoulli_process.htm');returnfalse;">binomialexperimentisaseriesofnindependenttrials,eachwithtwopossibleoutcomes(oftenlabeled"success"and"failure"),withaconstantprobability,p,ofsuccess.Thetotalnumberofsuccesses,k,isgivenbythebinomialdistribution.

Iftherearemorethantwopossibleoutcomes,usethemultinomialdistribution.

Ifthesamplingiswithoutreplacement,usethehypergeometricdistribution

Forlargen,andpnottoocloseto0or1,thebinomialdistributioncanbeapproximatedbyanormaldistributionwithmean =np,andvariance=np(1-p).Forlargen,andpcloseto0,itcanbeapproximatedbyaPoissondistributionwithparameter =np.Asn->infinitythesearethelimitingdistributions(providingp=constantinthenormalcase,andp->0,np=constantinthePoissoncase).

PoissonDistribution (discreteprobabdistforequations)

Usage: PoissonDist(k, )

Definition: exp(- )* ^k/k!=exp(- +k*log( )-log(k!))

Required: >0kisaninteger

Support: k 0

Moments: mean= ^2=1=1/sqrt( ) 2=3+1/

Ifeventsoccurbya=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Poisson_process.htm');returnfalse;">Poissonprocess,thenthenumberofeventsthatoccurinafixedtimeintervalisdescribedbythePoissondistribution(where istheaveragenumberofeventsperunittime).

HypergeometricDistribution (discreteprobabilitydist.forequations)

Usage: HypergeometricDist(k,n,s,N)

Definition: binomial(s,k)binomial(N-s,n-k)/binomial(N,n)Definitionof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_binomial_coefficient.htm');returnfalse;">binomial

Required: N 00 n N0 s Nk,N,nandsareintegers

Support: 0 k n

Moments: =ns/N^2=ns(1-s/N)(N-n)/[N(N-1)]1=(N-2s)(N-2n)sqrt(N-1)/[(N-2)sqrt(ns(N-s)(N-n))]2=N^2(N-1)/[(N-2)(N-3)ns(N-s)(N-n)][N(N+1)-6n(N-n)+3s(N-s)/N^2[N^2(n-2)-Nn^2+6n(N-n)]]

Thisprovidestheprobabilitythattherearek"successes"inarandomsampleofsizen,selected(withoutreplacement)fromNitemsofwhichsarelabeled"success"andN-slabeled"failure".

Itisusedinplaceofthebinomialdistributionforsituationswhichsamplewithoutreplacement.

NegativeBinomialDistribution (discreteprobabilitydist.forequations)

Usage: NegBinomialDist(k,n,p)

Definition: binomial(n+k-1,k)p^n(1-p)^kDefinitionof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_binomial_coefficient.htm');returnfalse;">binomial.

Required: 0 n0<p 1kandnareintegers

Support: 0 k

Moments: =n(1-p)/p^2=n(1-p)/p^21=(2-p)/sqrt(n(1-p))2=3+[p^2+6(1-p)]/(n(1-p))

Thisisthedistributionofthenumberoffailuresthatoccurinasequenceoftrialsbeforensuccesseshaveoccurred,ina=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bernoulli_process.htm');returnfalse;">Bernoulliprocess(independenttrials,withoutcomeslabeled"success"or"failure",andconstantprobabilitypofsuccess).

Thelimitofanegativebinomialdistributionasn ,(1-p) 0,n(1-p) ,isaPoissondistributionwithparameter .

Ifn=1,thenthisdistributionisjustthegeometricdistribution.

GeometricDistribution (discreteprobabilitydist.forequations)

Usage: GeometricDist(k,p)

Definition: p(1-p)^k

Required: 0<p 1kisaninteger

Support: 0 k

Moments: =(1-p)/ps^2=(1-p)/p^21=(2-p)/sqrt(1-p)2=3+[p^2+6(1-p)]/(1-p)

Thisdistributiondescribesthenumberof=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_Bernoulli_process.htm');returnfalse;">Bernoullitrials(independenttrials,withoutcomeslabeled"success"or"failure",andconstantprobabilitypofsuccess)beforethefirstsuccessoccurs(i.e.,includesonlythefailuretrials).Anexamplewouldbethenumberofcoinflipsresultingintailsbeforethefirstheadisseen.

SituationswhereBernoullitrialsarerepeateduntilthenthsuccessarecalled"negativebinomialexperiments",andthegeometricdistributionisaspecialcaseofthenegativebinomialdistributionwithn=1.

Notethatthegeometricdistributionisinsteaddefinedbysomeauthorstohavethe=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_pdf.htm');returnfalse;">pdf:p(1-p)^(k-1)

LogarithmicDistribution (discreteprobabilitydist.forequations)

Usage: LogarithmicDist(k,p)

Definition: -(p^k)/(klog(1-p))

Required: 0<p<1kinteger

Support: k 1

Moments: =-p/[(1-p)log(1-p)]

^2=-p(p+log(1-p))/[(1-p)log(1-p)]^2

Alsoknownasthe"logarithmicseriesdistribution".

MultinomialDistribution (discreteprobabilitydist.forequations)

Usage: MultinomialDist(bc,n,k1,p1,k2,p2,...km,pm)

Required: n 0ki 00 pi 1sumpi!=0bcbooleann,kiinteger

Support: n=sumki

Mean: E[ki]=npi

Covariance: cov[ki,kj]=-npipjifi!=jifi=jthencov[ki,ki]=var[ki]=npi(1-pi)

Themultinomialdistributionisageneralizationofthebinomialdistributiontothesituationwheretherearenotjusttwooutcomes(usuallylabeled"success"and"fail"),butrathermoutcomes,eachhavingprobabilitypi(i=1..m),andweareinterestedinthenumberofoccurrencesofeachoutcome(ki),giventhatatotalofntrialsareperformed.

Tocreateamultinomialdistributionbetweenthekiandnnodes,firstaddtothenetanew=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleannode,inthisexamplecalledbc.Thenaddlinksfromthenodesofallthenon-fixedparameters(usuallynandallki)tonodebc.Atnodebc,putanequationwithMultinomialDist,andconverttheequationtoatable.Finally,givenodebca=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_finding.htm');returnfalse;">findingoftrue.Normallythesumofpiisone,butNeticawilljustnormalizethepiifthatisnotthecase.Ifmis2,thenk2isdeterministicallydeterminedbyk1(i.e.,k2=n-k1),andk1isdistributedbyBinomialDist.Eachofthekiseparatelyhasabinomialdistributionwithparametersnandpi,andbecauseoftheconstraintthatthesumoftheki'sisn,theyarenegatively

correlated.TheDirichletdistributionistheconjugatepriorofthemultinomialinBayesianstatistics.Forassistanceonusingthisfunction,=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_email.htm');returnfalse;">contactoursupportteam.

Noisy-AndDistribution (DMprob.dist.forequations)

Usage: NoisyAndDist(e,inh,b1,p1,...bn,pn)

Definition: P(e)=(1-inh)producti=1ton(bi?1:(1-pi))

Required: 0 inh 1e,biBoolean0 pi 1

Usethisdistributionwhenthereareseveralpossiblerequirementsforanevent,andeachhasaprobabilitythatitwillactuallybenecessary.Eachofthenecessaryrequirementsmustpassfortheeventtooccur.Eventhen,thereisaprobability(givenbyinh)thattheeventmaynotoccur(makeinhzerotoeliminatethis).

Eachbiisa=4&&typeof(BSPSPopupOnMouseOver)=='function')BSPSPopupOnMouseOver(event);"class="BSSCPopup"onclick="BSSCPopup('X_PU_boolean_node.htm');returnfalse;">booleanvariable,whichwhenTRUE,indicatesarequirementpassed.eisalsoaboolean,whichindicateswhethertheeventoccurs.Eachofthepiaretheprobabilitythatbiwillberequiredtocausee.

Ifinhiszero,andonlyonepossiblerequirementisFALSE,saybk,thentheprobabilityforeis1-pk.IfmorepossiblerequirementsareFALSE,theprobabilitywillbelower.Andifinhisnonzero,theprobabilitywillbelower.ReducingapialwaysresultsinthesameorhigherP(e).

picanbeconsideredthe“strength”oftherelationbetweeneandbi,withzeroindicatingindependence(linkcouldberemoved),and1indicatingmaximumeffect.

SeealsoNoisyOrDist.

Noisy-MaxDistribution (multivariatedist.forequations)

SeealsoNoisyOrDist,NoisySumDist.

Forinformationonusingthisfunction,contactNorsys,andaskforthedocumenttitled"NoisyOr,Max,Sum.doc".

Noisy-SumDistribution (multivariatedist.forequations)

SeealsoNoisyMaxDist.

Forinformationonusingthisfunction,contactNorsysandaskforthedocumenttitled"NoisyOr,Max,Sum.doc".

CSVfileisacommonlyusedtermforaformofcasefileinwhichthenamesofthevariablesappearonthefirstline,andthenbelowareallthecases(i.e.records),witheachcaseonasinglelineandhavingavalueforeachofthevariables,andwithallthevaluesandvariablesintextformandseparatedbycommas(i.e."CommaSeparatedValues").Seealsotabdelimitedtext.

Tabdelimitedtextfileisacommonlyusedtermforaformofcasefileinwhichthenamesofthevariablesappearonthefirstline,andthenbelowareallthecases(i.e.records),witheachcaseonasinglelineandhavingavalueforeachofthevariables,andwithallthevaluesandvariablesintextformandseparatedbytabcharacters.SeealsoCSVfile.

AtextfileconsistsonlyofASCIIcharacters.Ithasnospecialsymbols,noformatting(bold,italics,fontsorsizes),nostructure(paragraphsections,chaptersections,margins,etc.),andnospecialinserts(pictures,tables,etc.).Youcancreateormodifyatextfileusingatexteditor.

ASCIIisatextcharacterencodingbasedontheEnglishalphabet,andwasfirstreleasedasastandardin1967.Itrepresentseachcharacterwith7bits,althoughtherearemany8-bitextensionsofit.ASCIIanditsextensionshavebeenbyfarthedominantwaytorepresenttextinacomputer,butarenowbeingovertakenbyUnicode,whichcanrepresentmanymorecharacters.InNetica,identifiers(i.e.IDnames)arealwayscomposedonlyofASCIIcharacters,whiletitlesanddescriptionsmaybeinUnicode.

LogisticDistribution (continuousprobabdistforequations)

Usage: LogisticDist(x, , )

Definition: exp(-(x- )/ )/( *(1+exp(-(x- )/ ))^2)

Parameters: =location =scale

Required: >0

Moments: Mean=Median=Mode=

variance=(pi* )^2/3

kurtosis=6/5

entropy=log( )+2

Itresemblesthenormaldistributioninshapebuthasheaviertails(higherkurtosis).Itscumulativedistributionfunction(cdf)isthelogisticfunction.