brief explanation of mcmc implementation in lalsuite hyung won lee, inje university with chunglee...

11th KAGRA f2f Meeting, 4-7 February 2015

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Brief Explanation of MCMC implementation

in lalsuiteHyung Won Lee, Inje University

with Chunglee Kim(KHU&KISTI) and Jeongcho Kim(Inje)

6 Feb. 2015, KAGRA f2f meeting, Hongo Campus

2015-2-6


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Motivation CBC gravitational wave sources Parameter Estimation with Bayesian

Inference Implementation in lalsuite Suggestions for KAGALI Discussions

Contents

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How does it work parameter estima-tion

Understanding Bayesian inference/MCMC

Which physical parameters How it was implemented in lalsuite How it could be implemented for

KAGALI Get practical work out items

Motivation

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Neutron star(NS) + Black hole(BH) binary

Mass range : Frequency range : Waveform : Inspiral, Merger, Ring-

down

CBC GW sources

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CBC Inspiral GW Waveform

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TaylorT1, 2, 3, 4 PadeT1 : P-approximation EOB : effective one body SpinTaylorT1, 2, 3, 4, 5 IMRPhenomA, B, C

Time Domain Template

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TaylorF1 TaylorF2 : standard for detection pipe-

line, SPA approximation TaylorF2Amp : include higher harmon-

ics due to amplitude corrections up to 2.5 pN

PadeF1 BCV BCVSpin

Frequency Domain Tem-plate

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Arun et.al., PRD79, 104023(2009) Amplitude corrections up to n=5

(2.5pN)

TaylorF2Amp Waveform

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Phase corrections up to 3.5PN (s-tandard in LAL)

SPA phase factor

+

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SPA phase factor(Code)

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Individual masses Luminosity distance Inclination angle Coalescence phase Coalescence time at geocenter Declination Right ascension Polarization Spins, quadrupole deformations

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Physical Parameters


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Bayesian Inference

• : unobservable model parameters• : observable data• : Joint probability observing data with

model parameter

Metropolis-Hasting Algorithm, samples

Parameter Estimation with Bayesian in-ference

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Parameter Estimation with Bayesian in-ference

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MCMC Samples

PTMCMCOutput.00PTMCMCOutput.nn

Post Process

cbcByesPostProc.py


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Network SNR

Overlap CalculationDataTemplate

One-sided power spectral density of noise

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ℒ (𝑠∨𝜃)∝exp [−2∫0

∞ |~𝑠 ( 𝑓 )−~h(𝜃 , 𝑓 )|2

𝑆𝑛 ( 𝑓 )𝑑𝑓 ]

Likelihood Calculation

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Unnormalized

Normalized

Various Overlaps

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Accept next state with probability

Metropolis-Hasting smapling

MCMC Process

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Use few chains with different tem-perature

Use likelihood Improve convergence Improve mixing The higher temperature, the

smoother distribution

Parallel Tempering

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𝑇 >1


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LAL MCMC Pipeline Directory structure of lalsuite

Implementation in lalsuite

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Post Processing python script

Basic entities of LALSuite

LAL applications

Simulation related functions and waveforms

Likelihood, proposal and prior functions


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LAL MCMC PipelineStart

End

Initialization

MPI synchro-nize

PT MCMC

Clearance

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ProcessParamsTable *commandLine; /** A ProcessParamsTable with command line arguments */

LALInferenceInitModelFunction initModel; /** A function that returns a new set of variables for the model */

LALInferenceAlgorithm algorithm; /** The algorithm function */ LALInferenceEvolveOneStepFunction evolve;

/** The algorithm's single iteration function */ LALInferencePriorFunction prior; /** The prior for the parameters */ LALInferenceCubeToPriorFunction CubeToPrior;

/** MultiNest prior for the parameters */ LALInferenceLikelihoodFunction likelihood;

/** The likelihood function */ LALInferenceProposalFunction proposal; /** The proposal function */ LALInferenceLogFunction logsample; /** Log sample, i.e. to disk */ LALInferenceTemplateFunction templt;

/** The template generation function */ … more

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LALInferenceRunState


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LAL MCMC pipeline in a glance

MCMC main main(start)

end

PTMCMCAlgorithm

parseCommandLine OptionsInitialize Rusnstate

initializeMCMCaddVariablesInitializeCBC

Initialize likelihoodInitialize MCMC state

MPI_Barrierwait synchronization

runState ->alogorithmmain MCMC routine

DeinitializeClean resources

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PTMCMCAlgorithm

end

PTMCMCAlgo-rithm(start)

PTMCMCOneStep

MPI setup, runComplete = 0Ladder setup for parallel tempering Ladder[i] = Min

Set temperature for this chainif(MPI_rank == 0) output

Anealing related setupDebug related setup

runState ->evolveOneStep MCMC routine

If(MPI_rank≠0) non-blocking re-ceive

MPI_Barrier

!runCom-plete

Ladder update if needCalculate ACL(autocorrelation length) If( i>Neff) runCom-

plete=1Anealing

post-anealing

Save for every Nskip stepIf(i>Niter) runComplete=1

If(MPI_rank==0 && runComplete==1) send run complete value to all other paral-lel process

MPI_BarrierXLALFree() resource

free

Receive runComplete state from root process

NoYes

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PTMCMCOneStep

PTMCMCOn-eStep(start)

MPI setup

runState ->proposal

Compute prior & likelihooddetermine acceptance probability

Accept

end

LALInferenceCyclicProposal

LALInferenceCyclicProposal LALInferenceCyclicPro-posal(start)

LALInferenceProposalFunction *cycle = NULL

Must have cycle array and cycle array length in propArgs

(cycle[i])(runState, proposedParams)Call proposal

end

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Call TaylorF2Amp in MCMC

Mcmc main

PTMCMCAlgorithm()

PTMCMCOn-eStep()

LALInferenceUndecom-posed

FreqDomainLogLikelihood()

LALInferenceTemplateXLALSimInspiralChooseWave-

form()

XLALSimInspiralChooseFDWaveformFromCache()

XLALSimInspiralChooseFDWave-form()

XLALSimInspiralTaylor-F2Amp()

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1. waveform library [LALSimulation]

2. PE library [LALInference & LALapps]

3. basic libraries are scattered, but most basic ones are in [LAL]

LAL parameter estimation(PE) pipeline

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LALSimulation/src/ ..

LALSimInspiral.h -> protocol definitionsXLALSimInspiralF2AmpPlus() -> XLALSimInspiralF2AmpCross() ->

LALSimInspiral.c -> XLALSimInspiralChooseFDWaveform() call a waveform model XLALSimInspiralF2AmpPlus()XLALSimInspiralF2AmpCross()

LALSimInspiralTaylorF2Amp.c -> example of a FD waveform

XLALSimInspiralF2AmpPlus()XLALSimInspiralF2AmpCross()

waveform library [LALSimulation]

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LALInference/src/..

LALInference.h LALInferenceReadData.cLALInferecneTemplate.c

LALInference.h -> collections of structures

typedef tagLALInferenceRunState signal/parameters{

∙∙∙ -> Structure to contain inference run state} LALInferenceRunState;

typedef struct tagLALInferenceIFOData data for detector including sensitivity{

∙∙∙ -> Structure to contain IFOdata} LALInferenceIFOData;

PE library [LALInference]

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LALInference/src/..


reads injection parameters from an xml file reads PSD for each detector reads data for each detector generate noise for each detector

LALInferenceIFOData *LALInferenceReadData(ProcessParamsTable *commandLine)-> Read in the data and store it in a LALInferenceIFOData structure


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LALInference/src/..


- Jump around parameter space generate template signal

LALInferenceTemplate.c -> template calls to LAL template functions

LALInferenceTemplateXLALSimInspiralChooseWaveform() Wrapper for LALSimulation waveforms : XLALSimInspiralChooseFDWaveform()

XLALSimInspiralChooseTDWaveform()- Parameters of non-spinning waveform in LALInferencePrior.c


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PE library [LALInference]LALInference/src/..

LALInference.h LALInferenceLikelihood.cLALInferecneTemplate.c

LALInferenceLikelihood.c -> Bayesian Followup likelihood function

LALInferenceUndeomposedFreqDomainLogLikelihood()Required (`currentParams') parameters are:

"rightascension" (REAL8, radian, 0 <= RA <= 2pi) "declination" (REAL8, radian, -pi/2 <= dec <=pi/2) "polarisation” (REAL8, radian, 0 <= psi <= pi) "time" (REAL8, GPS sec.)


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PE library [LALapps]

LALapps/src/inspiral/posterior/..

LALInferenceMCMC.cLALInferenceMCMCSampler.c

LALInferenceMCMC.c -> Bayesian Followup function testing site

main() 1. Set up structures for MCMC 2. Choose the likelihood function -> ex) student-T , Undecomposed. 3. Call MCMC algorithm -> sampling posterior function


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PE library [LALapps]

LALapps/src/inspiral/poste-rior/..

LALInferenceMCMC.cLALInferenceMCMCSampler.c

LALInferenceMCMCSampler.c -> Bayesian Followup, MCMC algorithm

PTMCMCAlgorithm() PTMCMCOneStep() -> Metropolis-Hasting algorithm implemented


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basic functions, librarieslal/FrequencySeries.h -> dataStructurelal/LALDatatypes.h ->Primitive datatypes

Aggregate datatypes Store arbitrarily large sets or collections of primi-

tive datatypes. aggregate datatypes are defines

Structured datatypes : embed primitive and ag-gregate datatypes

inside structures that define their physical mean-ing.

lal/LALConstants.h -> physical constants, Pi, h, G, etc.


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Directory structure by functionality• MCMC chain generation• Waveform generation• Input output functions

Notes to consider• Waveform function call parameter• Post process language• Python• Haskell• C and gnuplot

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Suggestions for KAGALI


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Bayesian Parameter Estimation Optimal library structure How to post process? All from scratch?

Collaboration meeting from 9 to 11 February at Inje University

Discussions

2015-2-6

brief explanation of mcmc implementation in lalsuite hyung won lee, inje university with chunglee...

Documents

th kagra f2f meeting

mcmc process

lalsuite suggestions

lalsuite hyung

phase corrections

lal spa phase factor

mcmc samples ptmcmcoutput

spa phase factorcode