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geoR : Package for Geostatistical Data Analysis

An illustrative session

Paulo J. Ribeiro Jr. & Peter J. Diggle

Last update: November 21, 2006

1 Itrodu!tio

2 "tartig a "essio ad Loadig Data

2.1 Loadig t#e pa!$age

2.2 %sig data

'(plorator) *ools

.1 Plottig data lo!atios ad values

.2 'mpiri!al variograms

+ Parameter 'stimatio -ross/alidatio

6 "patial Iterpolatio

a)esia al)sis

3 "imulatio o4 5aussia Radom ields

7 -itig geoR

1 Introduction

*#e pa!$age geoR provides 4u!tios 4or geostatisti!al data aal)sis usig t#e

so4t8are R. *#is do!umet illustrates some 9but ot all; o4 t#e !apabilities o4 t#epa!$age.

*#e ob


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*)pi!all), de4ault argumets are used 4or t#e 4u!tio !alls ad t#e user is

e!ouraged to ispe!t ot#er argumets o4 t#e 4u!tios usig

t#e args ad help 4u!tios. or ista!e, to see all t#e argumets 4or t#e

4u!tiovariog t)pe args(variog) ad@or help(variog).

*#e !ommads s#o8 i t#is page are also available i t#e?le http://www.leg.ufpr.br/geoR/geoRdoc/geoRintro.R.

>e re4er to t#e geoR do!umetatio

9http://www.leg.ufpr.br/geoR/geoR.html#help; 4or more details

o t#e 4u!tios i!luded i t#e pa!$age geoR.

Ae(tB A4rotB AupB

2 Starting a Session and Loading Data

2.1 Loading the package

4ter startig a R sessio, load geoR 8it# t#e

!ommad library 9or require;. I4 t#e pa!$age is loaded !orre!tl) a

message 8ill be displa)ed.

> library(geoR)

I4 t#e istallatio dire!tor) 4or t#e pa!$age is t#e de4ault lo!atio

4or Rpa!$ages, t)pe:

> library(geoR, lib.loc="PA!#geoR")

8#ere C!"$%&%geoR= is t#e pat# to t#e dire!tor) 8#ere geoR 8as

istalled.

2.2 Using data

*)pi!all), data are stored as a ob


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>e re4er to t#e do!umetatio 4or t#e

4u!tios as.geodata ad read.geodata 4or more i4ormatio o #o8

to import@!overt data ad o t#e de?itios 4or t#e !lass geodata.

-#e!$http://www.leg.ufpr.br/geoR/importing"**.html4or

i4ormatio o #o8 to read data 4rom a "-II 9te(t; ?le.

*#ere a a 4e8 datasets i!luded i t#e pa!$age distributio. or t#e e(amples

i!luded i t#is do!umet 8e use t#e data set s+,, i!luded i

t#e geoR distributio. *o load t#is data t)pe:

> data(s$%%)

*#e list o4 all datasets i!luded i t#e pa!$age is give

b) data(package-geoR).

Ae(tB AprevB AprevtailB A4rotB AupB

ommands in the geoRintro webpage## #### his is a script file illustrating some features of geoR## *t may be used as an introduction to usage of geoR#### &nly a few key commands and options are illustrated here.## his is 0& an e1austive demonstration of the package resources.##

## he commands are for illustrative purposes only.## 2e do not attempt to perform a definitive analysis of the data.###### +. ourcing the package#### uncomment one of the following inf necessaryrequire(geoR)##library(geoR3 lib.loc-!"$%&%geoR)

data(s+,,)par.ori 4 par(no.readonly-R56)

#### 7. 8escriptive plots####9peg(s+,,plot/s+,,p,+.9peg3 wid-;,3 hei-;,)plot(s+,,)##dev.off()####9peg(s+,,plot/s+,,p,7.9peg3 wid-;,3 hei-;,)par(mfrow - c(737)3 mar-c(


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points(s+,,3 1lab - oord >3 ylab - oord ?3 pt.divide - rank.prop)points(s+,,3 1lab - oord >3 ylab - oord ?3 ce1.ma1 - +.@3 col -gray(seq(+3 ,.+3 l-+,,))3 pt.divide - equal)points(s+,,3 pt.divide - quintile3 1lab - oord >3 ylab - oord ?)##dev.off()par(par.ori)

####


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##9peg(s+,,plot/s+,,p,;a.9peg3 wid-;,,3 hei-7@;)par(mfrow-c(+37)3mar-c(


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legend(,.;;3 ,.


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save.image()##

##9peg(s+,,plot/s+,,p,=a.9peg3 wid-;,,3 hei-=,,)par(mfcol - c(;37)3 mar-c(7.;37.;3.;3.;)3 mgp-c(+.=3,.=3,))plot(1v.wls)##dev.off()

par(par.ori)#### =. Jriging####9peg(s+,,plot/s+,,p,K.9peg3 wid-


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##9peg(s+,,plot/s+,,p+7.9peg3 wid-


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## +,. imulation##sim+ 4 grf(+,,3 cov.pars-c(+3 .7;))

##9peg(s+,,plot/s+,,p+;.9peg3 wid-;,,3 hei-7;,)par(mfrow-c(+37)3mar-c(7.;37.;3+3,.7)3mgp-c(+.;3.=3,))points.geodata(sim+3 main-simulated data)

plot(sim+3 ma1.dist-+3 main-true and empirical variograms)##dev.off()

sim7 4 grf(+3 grid-reg3 cov.pars-c(+3 .7;))

##9peg(s+,,plot/s+,,p+B.9peg3 wid-


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8ata summary

Fin. +st Su. Fedian Fean


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!igure

1"

Plot produced

by plot.geodata.

*#e 4u!tio points.geodata produ!es a plot s#o8ig t#e data

lo!atios. lterativel), poits idi!atig t#e data lo!atios !a be added to a

!urret plot. *#ere are optios to spe!i4) poit siFes, patters ad !olors, 8#i!#

!a be set to be proportioal to t#e data values or spe!i?ed Euatiles. "ome

e(amples o4 grap#i!al outputs are illustrated b) t#e !ommads belo8 ad

!orrespodig plots as s#o8 i igure .1.

> par(mfrow = c(&, &))

> points(s$%%, 'lab = "oord ", ylab = "oord *")

> points(s$%%, 'lab = "oord ", ylab = "oord *",

+ pt.diide = "ran-.prop")

> points(s$%%, 'lab = "oord ", ylab = "oord *",

+ ce'.ma' = $., col = gray(se/($, %.$, l = $%%)),

+ pt.diide = "e/ual")
http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose3.html#x4-60003.1http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose3.html#x4-60003.1


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> points(s$%%, pt.diide = "/uintile", 'lab = "oord ",

+ ylab = "oord *")

!igure

2"

Plot produced

by points.geodata.

3.2 E#pirical ariogra#s

'mpiri!al variograms are !al!ulated usig t#e 4u!tio variog. *#ere are

optios 4or t#e classical or modulus estimator. Results !a be retured as

variogram !louds, bied or smoot#ed variograms. *#ere are met#ods

4or plot to 4a!ilitate t#e displa) o4 t#e results as s#o8 i igure .

> cloud$ 01 ariog(s$%%, option = "cloud", ma'.dist = $)

> cloud& 01 ariog(s$%%, option = "cloud", estimator.type = "

modulus",
http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose3.html#x4-70233http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose3.html#x4-70233


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+ ma'.dist = $)

> bin$ 01 ariog(s$%%, uec = se/(%, $, l = $$))

> bin& 01 ariog(s$%%, uec = se/(%, $, l = $$),

+ estimator.type = "modulus")

> par(mfrow = c(&, &))> plot(cloud$, main = "classical estimator")

> plot(cloud&, main = "modulus estimator")

> plot(bin$, main = "classical estimator")

> plot(bin&, main = "modulus estimator")

!igure

3"

Ploting

of variog results.

"everal results are retured b) t#e 4u!tio variog. *#e ?rst t#ree are t#e

more importat oes ad !otais t#e dista!es, t#e estimated semivaria!e ad

t#e umber o4 pairs 4or ea!# bi.


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> names(bin$)

N+O u v

N bin& 01 ariog(s$%%, uec = se/(%, $, l = $$),+ estimator.type = "modulus", bin.cloud = )

> par(mfrow = c($, &))

> plot(bin$, bin.cloud = , main = "classical estimator")

> plot(bin&, bin.cloud = , main = "modulus estimator")
http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose3.html#x4-70003.2http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose3.html#x4-70003.2


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!igure

$"

2o'1plots for each of the

ariogram bins.

Dire!tioal variograms !a also be !omputed b) t#e 4u!tio variog usig

t#e argumets Cdirection= ad Ctolerance=. or e(ample, to !ompute a

variogram 4or t#e dire!tio 60 degrees 8it# t#e de4ault tolera!e agle 922.

degrees; t#e !ommad 8ould be:

> ario3% 01 ariog(s$%%, ma'.dist = $, direction = pi45)

or a Eui!$ !omputatio i 4our dire!tios 8e !a use t#e

4u!tio variog 8#i!# b) de4ault !omputes variogram 4or t#e dire!tio

agles 0o, +o, 70oad 1o.

> ario.6 01 ariog6(s$%%, ma'.dist = $)

*#e igure s#o8 t#e dire!tioal variograms obtaied 8it# t#e !ommadsabove.

> par(mfrow = c($, &), mar = c(5, 5, $.7, %.7))

> plot(ario3%)

> title(main = e'pression(paste("directional, angle = ",


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+ 3% 8 degree)))

> plot(ario.6, lwd = &)

!igure

%"

9irectional

ariograms

$ Para#eter Esti#ation

*#eoreti!al ad empiri!al variograms !a be plotted ad visuall) !ompared. or

e(ample, t#e le4t pael i igure 6s#o8s t#e t#eoreti!al variogram model used tosimulate t#e data s+,, ad t8o estimated variograms.

> bin$ 01 ariog(s$%%, uec = se/(%, $, l = $$))

> plot(bin$)

> lines.ariomodel(co.model = "e'p", co.pars = c($,

+ %.5), nugget = %, ma'.dist = $, lwd = 5)

> smooth 01 ariog(s$%%, option = "smooth", ma'.dist = $,

+ n.points = $%%, -ernel = "normal", band = %.&)> lines(smooth, type = "l", lty = &)

> legend(%.6, %.5, c("empirical", "e'ponential model",

+ "smoothed"), lty = c($, $, &), lwd = c($,

+ 5, $))


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I pra!ti!e 8e usuall) do=t $o8 t#e true parameters 8#i!# #ave top be

estimated b) some met#od. I t#e pa!$age geoR t#e model parameters !a be

estimated:

$. by eye: trying different models oer empirical ariograms

(using the function lines.variomodel),

&. by least squares fit of empirical variograms: with optionsfor ordinary (#;


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!igure

&"

heoretical ariogram cures added to empirical

ariograms.

>#e usig t#e parameter estimatio

4u!tios variofit ad likfit t#e ugget e44e!t parameter !a eit#er be

estimated or set to a ?(ed value. *#e same applies 4or smoot#ess, aisotrop)

ad tras4ormatio parameters. ptios 4or ta$ig treds ito a!!out are also

i!luded. *reds !a be spe!i?ed as pol)omial 4u!tios o4 t#e !oordiates

ad@or liear 4u!tios o4 give !ovariates.

e(ample !all to likfit is give belo8. Ket#ods

4or print() ad summary() #ave bee 8ritte to summariFe t#e resultig

ob ml 01 li-fit(s$%%, ini = c($, %.7))

likfit: likelihood ma1imisation using the function o

ptim.

likfit: 5se control() to pass additional

arguments for the ma1imisation function.


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Dor further details see documentation for op

tim.

likfit: *t is highly advisable to run this function

several

times with different initial values for theparameters.

likfit: 2"R0*0T: his step can be time demandingU

likfit: end of numerical ma1imisation.

> ml

likfit: estimated model parameters:

beta tausq sigmasq phi

,.@@BB ,.,,,, ,.@;+@ ,.+=7@

likfit: ma1imised loglikelihood - = summary(ml)

ummary of the parameter estimation

6stimation method: ma1imum likelihood

!arameters of the mean component (trend):

beta

,.@@BB

!arameters of the spatial component:

correlation function: e1ponential

(estimated) variance parameter sigmasq (partia

l sill) - ,.@;+@


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(estimated) cor. fct. parameter phi (range par

ameter) - ,.+=7@

anisotropy parameters:

(fi1ed) anisotropy angle - , ( , degrees )

(fi1ed) anisotropy ratio - +

!arameter of the error component:

(estimated) nugget - ,

ransformation parameter:

(fi1ed) Lo1o1 parameter - + (no transformati

on)

Fa1imised Gikelihood:

log.G n.params "* L*

= options(geoR.messages = A;


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> ml 01 li-fit(s$%%, ini = c($, %.7), fi'.nugget = )

> reml 01 li-fit(s$%%, ini = c($, %.7), fi'.nugget = ,

+ method = "R;")

> ols 01 ariofit(bin$, ini = c($, %.7), fi'.nugget = ,+ weights = "e/ual")

> wls 01 ariofit(bin$, ini = c($, %.7), fi'.nugget = )

itting models with a B'ed alue for the nugget

> ml.fn 01 li-fit(s$%%, ini = c($, %.7), fi'.nugget = ,

+ nugget = %.$7)

> reml.fn 01 li-fit(s$%%, ini = c($, %.7), fi'.nugget = ,+ nugget = %.$7, method = "R;")

> ols.fn 01 ariofit(bin$, ini = c($, %.7), fi'.nugget = ,

+ nugget = %.$7, weights = "e/ual")

> wls.fn 01 ariofit(bin$, ini = c($, %.7), fi'.nugget = ,

+ nugget = %.$7)

itting models estimated nugget

> ml.n 01 li-fit(s$%%, ini = c($, %.7), nug = %.7)

> reml.n 01 li-fit(s$%%, ini = c($, %.7), nug = %.7,

+ method = "R;")

> ols.n 01 ariofit(bin$, ini = c($, %.7), nugget = %.7,

+ weights = "e/ual")

> wls.n 01 ariofit(bin$, ini = c($, %.7), nugget = %.7)

No8, t#e !omads 4or plottig ?tted models agaist empiri!al variogram as

s#o8 i igure +are:

> par(mfrow = c($, 5))

> plot(bin$, main = e'pression(paste("fi'ed ", tauD& ==

+ %)))

> lines(ml, ma'.dist = $)
http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose4.html#x5-80004http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose4.html#x5-80004http://www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose4.html#x5-80004


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*8o $ids o4 variogram envelopes !omputed b) simulatio are illustrated i

t#e ?gure belo8.

*#e plot o t#e le4t#ad side s#o8s a evelope based o permutatios o4

t#e data values a!ross t#e lo!atios, i.e. evelopes built uder t#e assumptio o4

o spatial !orrelatio. *#e evelopes s#o8 o t#e rig#t#ad side are based osimulatios 4rom a give set o4 model parameters, i t#is e(ample t#e parameter

estimates 4rom t#e >L" variogram ?t. *#is evelope s#o8s t#e variabilit) o4 t#e

empiri!al variogram.

> en.mc 01 ariog.mc.en(s$%%, obE.ar = bin$)

> en.model 01 ariog.model.en(s$%%, obE.ar = bin$,

+ model = wls)


> plot(bin$, enelope = en.mc)

> plot(bin$, enelope = en.model)

!igure

("

Fariogram

enelopes.

Pro?le li$eli#oods 91D ad 2D; are !omputed b) t#e 4u!tio proflik.

Mere 8e s#o8 t#e pro?le li$eli#oods 4or t#e !ovaria!e parameters o4 t#e model


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8it#out ugget e44e!t previousl) ?tted b) likfit.

>RNIN5: R%NNIN5 *M' N'* -KKND -N ' *IK'

-N"%KIN5

> prof 01 profli-(ml, geodata = s$%%, sill.al = se/(%.6@,

+ &, l = $$), range.al = se/(%.$, %.7&, l = $$),

+ uni.only = A;


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-rossvalidatio residuals are obtaied subtra!tig t#e observed data mius t#e

predi!ted value. "tadardised residuals are obtaied dividig b) t#e sEuare root

o4 t#e predi!tio varia!e 9C$rigig varia!e=;. ) de4ault t#e 10 plots s#o8 i

t#e igure 10are produ!ed but t#e user !a restri!t t#e !#oi!e usig t#e 4u!tio

argumets.

> par(mfcol = c(7, &), mar = c(5, 5, $, %.7), mgp = c($.7,

+ %., %))

> plot('.wls)

!igure

1-"

ross1alidations

results

variatio o4 t#is met#od is illustrated b) t#e e(t t8o !alls 8#ere t#e model

parameters are reestimated ea!# time a poit is removed 4rom t#e dataset.


-N"%KIN5


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> 'R.ml 01 'alid(s$%%, model = ml, reest = RG?)

> 'R.wls 01 'alid(s$%%, model = wls, reest = RG?,

+ ariog.obE = bin$)

& Spatial Interpolation

-ovetioal geostatisti!al spatial iterpolatio 9kriging; !a be per4ormed 8it#

optios 4or:

$. Simple kriging

&. Ordinary kriging

5. Trend universal! kriging

6. "#ternal trend kriging

*#ere are additioal optios 4or o(-o( tras4ormatio 9ad ba!$

tras4ormatio o4 t#e results; ad aisotropi! models. "imulatios !a be dra8

4rom t#e resultig predi!tive distributios i4 reEuested.

s a ?rst e(ample !osider t#e predi!tio at 4our lo!atios labeled 1, 2, 3,

4 ad idi!ated i t#e ?gure belo8.

> plot(s$%%Hcoords, 'lim = c(%, $.&), ylim

= c(%,

+ $.&), 'lab = "oord ", ylab = "oord

*")

> loci 01 matri'(c(%.&, %.3, %.&, $.$, %.&, %

.5,

+ $, $.$), ncol = &)

> te't(loci, as.character($:6), col = "red")

> polygon(' = c(%, $, $, %), y = c(%, %, $,

$),

+ lty = &)


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!igure

11"

9ata locations and points to be

predicted

*#e !ommad to per4orm ordinary kriging usig t#e parameters estimated b)

8eig#ted least sEuares 8it# ugget ?(ed to Fero 8ould be:

> -c6 01 -rige.con(s$%%, locations = loci, -rige = -rige.control

(obE.m = wls))

*#e output is a list i!ludig t#e predi!ted values 9kc'predict; ad t#e

$rigig varia!es 9kc'krige.var;.

-osider o8 a se!od e(ample. *#e goal is to per4orm predi!tio o a grid

!overig t#e area ad to displa) t#e results. gai, 8e use ordiar) $rigig. *#e

!ommads !ommads belo8 de?es a grid o4 lo!atios ad per4orms t#e

predi!tio at t#ose lo!atios.

> pred.grid 01 e'pand.grid(se/(%, $, l = 7$), se/(%,

+ $, l = 7$))

> -c 01 -rige.con(s$%%, loc = pred.grid, -rige = -rige.control(

obE.m = ml))


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met#od 4or t#e 4u!tio image !a be used 4or displa)ig predi!ted values as

s#o8 i t#e e(t igure, as 8ell as ot#er predi!tio results retured

b) krige.conv.

> image(-c, loc = pred.grid, col = gray

(se/($, %.$,

+ l = 5%)), 'lab = "oord ", ylab =

"oord *")

!igure

12"

ap of the -riging

estimates

' ayesian /nalysis

a)esia aal)sis 4or 5aussia models is implemeted b) t#e

4u!tio krige.bayes. It !a be per4ormed 4or di44eret Hdegrees o4

u!ertait)H, meaig t#at model parameters !a be treated as ?(ed or radom.

s a e(ample !osider a model 8it#out ugget ad i!ludig u!ertait) i

t#e mea, sill ad rage parameters. Predi!tio at t#e 4our lo!atios idi!ated

above is per4ormed b) t)pig a !ommad li$e:


-N"%KIN5


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> bsp6 01 -rige.bayes(s$%%, loc = loci, prior = prior.control(phi

.discrete = se/(%,

+ 7, l = $%$), phi.prior = "rec"), output = output.control(n.po

st = 7%%%))

Mistograms s#o8ig posterior distributio 4or t#e model parameters !a be

plotted b) t)pig:

> par(mfrow = c($, 5), mar = c(5, 5, $, %.7), mgp = c(&,

+ $, %))

> hist(bsp6HposteriorHsampleHbeta, main = "", 'lab = e'

pression(beta),

+ prob = )

> hist(bsp6HposteriorHsampleHsigmas/, main = "",

+ 'lab = e'pression(sigmaD&), prob = )

> hist(bsp6HposteriorHsampleHphi, main = "", 'lab = e'p

ression(phi),

+ prob = )

!igure

13"

!istograms of samples from posterior

distribution

%sig summaries o4 t#ese posterior distributios 9meas, medias or modes;

8e !a !#e!$ t#e Hestimated a)esia variogramsH agaist t#e empiri!alvariogram, as s#o8 i t#e e(t ?gure. Noti!e t#at it is also possible to !ompare

t#ese estimates 8it# ot#er ?tted variograms su!# as t#e oes !omputed i "e!tio

.


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> plot(bin$, ylim = c(%, $.7))

> lines(bsp6, ma'.dist = $.&, summ = mean)

> lines(bsp6, ma'.dist = $.&, summ = median, lty =

&)

> lines(bsp6, ma'.dist = $.&, summ = "mode", post

= "par",+ lwd = &, lty = &)

> legend(%.&7, %.6, legend = c("ariogram posterior

mean",

+ "ariogram posterior median", "parameters post

erior mode"),

+ lty = c($, &, &), lwd = c($, $, &), ce' = %.@)

!igure

1$"

Fariogram models based on the posterior

distributions

*#e e(t ?gure s#o8s predi!tive distributios at t#e 4our sele!ted lo!atios.

Das#ed lies s#o8 5aussia distributios 8it# mea ad varia!e give b)

results o4 ordiar) $rigig obtaied i "e!tio +. *#e 4ull lies !orrespod to t#e

a)esia predi!tio. *#e plot s#o8s results o4 desit) estimatio usig samples4rom t#e predi!tive distributios.

> par(mfrow = c(&, &))

> for (i in $:6) I

+ -p' 01 se/(-c6HpredJiK 1 5 8 s/rt(-c6H-rige.arJiK),


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+ -c6HpredJiK + 5 8 s/rt(-c6H-rige.arJiK),

+ l = $%%)

+ -py 01 dnorm(-p', mean = -c6HpredJiK, sd = s/rt(-c6H-ri

ge.arJiK))

+ bp 01 density(bsp6HpredicHsimulJi, K)+ r' 01 range(c(-p', bpH'))

+ ry 01 range(c(-py, bpHy))

+ plot(cbind(r', ry), type = "n", 'lab = paste(";ocation",

+ i), ylab = "density", 'lim = c(16, 6),

+ ylim = c(%, $.$))

+ lines(-p', -py, lty = &)

+ lines(bp)

+ L

!igure

1%"

Predictie distributions at the four selected

locations


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!igure

1&"

aps obtained from the predictie

distribution

( Si#ulation o0 aussian ando# !ields

*#e 4u!tio grf geerates simulatios o4 5aussia radom ?elds o regular or

irregular sets o4 lo!atios. It relies o t#e de!ompositio o4 t#e !ovaria!e matri(

ad t#er4ore 8o=t 8or$ 4or large umber o4 lo!atios i 8#i!# !ase 8e suggest

t#e usage o4 t#e pa!$age Radomields. "ome o4 its 4u!tioalit) is illustrated

b) t#e e(t !ommads.


> sim$ 01 grf($%%, co.pars = c($, %.&7))

> points.geodata(sim$, main = "simulated locations and alues")

> plot(sim$, ma'.dist = $, main = "true and empirical ariograms")


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!igure

1'"

par(mfrow = c($, &))

> sim& 01 grf(66$, grid = "reg", co.pars = c($,

+ %.&7))

> image(sim&, main = "a small1ish simulation", col = gray(se/($,

+ %.$, l = 5%)))


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!igure

1("


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pages - M+;+=Q3

issn - M+B,K


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ee also Ycitation(pkgname)Y for citing R packages

.

Note: urther e'amples for the function krige.bayes are gien in

the

Ble http://www.leg.ufpr.br/geoR/geoRdoc/e1amples.krige.

bayes.R.

require(geoR)set.seed(7=;)#### Durther e1amples for the usage of krige.bayes()## #### Lefore reading this see documentation for krige.bayes

## H help(krige.bayes)#### 2"R0*0T: $66 "GG "0 L6 *F6 "08 !"*0T 86FF"08*0T

## imulating datae1.data 4 grf(;,3 cov.pars-c(+,3 .7;))

#### Lasic usage##

## a basic and simple call to the functione1.post 4 krige.bayes(e1.data)

e1.postnames(e1.post)

## different input and output optionse1+ 4 krige.bayes(e1.data3 prior - list(phi.prior - fi1ed3 phi - ,.


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e1.bayes 4 krige.bayes(e1.data3 loc-e1.grid3 prior - prior.control(phi.discrete-seq(,3 73 l-


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ap.kb

#### 0ow including tausq##! 4 prior.control(tausq.rel.prior - uni3 tausq.rel.discrete -seq(,3 .;3 l-B))

ap;.kb 4 krige.bayes(ap+)ap;.kb## using the previous posterior as prior for ne1t callapB.kb 4 krige.bayes(ap73 prior-post7prior(ap;.kb))apB.kb######! 4 prior.control(phi.prior-c(.73.


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par(op)

N#?: we recommend the

pac-age Randomields (http://cran.r

pro9ect.org/src/contrib/!"J"T6.html#RandomDields) for

a more comprehensie implementation for simulation of

Oaussian Random ields.

require(geoR)set.seed(7=;)#### Durther e1amples for the usage of krige.bayes()## #### Lefore reading this see documentation for krige.bayes## H help(krige.bayes)#### 2"R0*0T: $66 "GG "0 L6 *F6 "08 !"*0T 86FF"08*0T

## imulating datae1.data 4 grf(;,3 cov.pars-c(+,3 .7;))

#### Lasic usage##

## a basic and simple call to the functione1.post 4 krige.bayes(e1.data)e1.postnames(e1.post)

## different input and output optionse1+ 4 krige.bayes(e1.data3 prior - list(phi.prior - fi1ed3 phi - ,.


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plot(e1.bayes)lines(e1.bayes3 summ-median3 lty-73 post-par)lines(e1.bayes3 summ-mean3 lwd-73 lty-73 post-par)

## ... and for the predictiveop 4 par(no.readonly - R56)par(mfrow-c(737))

par(mar-c(


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apB.kb 4 krige.bayes(ap73 prior-post7prior(ap;.kb))apB.kb######! 4 prior.control(phi.prior-c(.73.

manual geor web

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