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Brief Explanation of MCMC implementation in lalsuite Hyung Won Lee, Inje University with Chunglee Kim(KHU&KISTI) and Jeongcho Kim(Inje) 6 Feb. 2015, KAGRA f2f meeting, Hongo Campus 11th KAGRA f2f Meeting, 4-7 February

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Motivation CBC gravitational wave sources Parameter Estimation with Bayesian Inference Implementation in lalsuite Suggestions for KAGALI Discussions Contents 11th KAGRA f2f Meeting, 4-7 February

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How does it work parameter estimation 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 11th KAGRA f2f Meeting, 4-7 February

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CBC GW sources 11th KAGRA f2f Meeting, 4-7 February

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CBC Inspiral GW Waveform 11th KAGRA f2f Meeting, 4-7 February

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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 11th KAGRA f2f Meeting, 4-7 February

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TaylorF1 TaylorF2 : standard for detection pipeline, SPA approximation TaylorF2Amp : include higher harmonics due to amplitude corrections up to 2.5 pN PadeF1 BCV BCVSpin Frequency Domain Template 11th KAGRA f2f Meeting, 4-7 February

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Arun et.al., PRD79, (2009) Amplitude corrections up to n=5 (2.5pN) TaylorF2Amp Waveform 11th KAGRA f2f Meeting, 4-7 February

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Phase corrections up to 3.5PN (standard in LAL) SPA phase factor + 11th KAGRA f2f Meeting, 4-7 February

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SPA phase factor(Code) 11th KAGRA f2f Meeting, 4-7 February

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Individual masses Luminosity distance Inclination angle Coalescence phase Coalescence time at geocenter Declination Right ascension Polarization Spins, quadrupole deformations th KAGRA f2f Meeting, 4-7 February Physical Parameters

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Parameter Estimation with Bayesian inference 11th KAGRA f2f Meeting, 4-7 February

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Parameter Estimation with Bayesian inference 11th KAGRA f2f Meeting, 4-7 February MCMC Samples PTMCMCOutput.00 PTMCMCOutput.nn Post Process cbcByesPostProc.py

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Overlap Calculation Data Template One-sided power spectral density of noise 11th KAGRA f2f Meeting, 4-7 February

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Likelihood Calculation 11th KAGRA f2f Meeting, 4-7 February

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Various Overlaps 11th KAGRA f2f Meeting, 4-7 February

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11th KAGRA f2f Meeting, 4-7 February MCMC Process

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Parallel Tempering 11th KAGRA f2f Meeting, 4-7 February

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LAL MCMC Pipeline Directory structure of lalsuite Implementation in lalsuite 11th KAGRA f2f Meeting, 4-7 February Post Processing python script Basic entities of LALSuite LAL applications Simulation related functions and waveforms Likelihood, proposal and prior functions

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11th KAGRA f2f Meeting, 4-7 February LAL MCMC Pipeline Start End Initialization MPI synchronize 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 th KAGRA f2f Meeting, 4-7 February LALInferenceRunState

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LAL MCMC pipeline in a glance MCMC main main (start) end PTMCMCAlgorithm parseCommandLine Options Initialize Rusnstate initializeMCMC addVariables InitializeCBC Initialize likelihood Initialize MCMC state MPI_Barrier wait synchronization runState ->alogorithm main MCMC routine Deinitialize Clean resources 11th KAGRA f2f Meeting, 4-7 February

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PTMCMCAlgorithm end PTMCMCAlgorithm (start) PTMCMCOneStep runState ->evolve OneStep MCMC routine If(MPI_rank≠0) non-blocking receive MPI_Barrier !runComplete Ladder update if need Calculate ACL(autocorrelation length) If( i>Neff) runComplete=1 Anealing post-anealing Save for every Nskip step If(i>Niter) runComplete=1 If(MPI_rank==0 && runComplete==1) send run complete value to all other parallel process MPI_Barrier XLALFree() resource free Receive runComplete state from root process No Yes 11th KAGRA f2f Meeting, 4-7 February

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PTMCMCOneStep (start) MPI setup runState ->proposal Compute prior & likelihood determine acceptance probability Accept end LALInferenceCyclicProposal (start) LALInferenceProposalFunction *cycle = NULL Must have cycle array and cycle array length in propArgs (cycle[i])(runState, proposedParams) Call proposal end 11th KAGRA f2f Meeting, 4-7 February

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Call TaylorF2Amp in MCMC Mcmc main PTMCMCAlgorithm() PTMCMCOneStep() LALInferenceUndecomposed FreqDomainLogLikelihood() LALInferenceTemplate XLALSimInspiralChooseWaveform() XLALSimInspiralChooseFD WaveformFromCache() XLALSimInspiralChooseFDWaveform() XLALSimInspiralTaylorF2Amp() 11th KAGRA f2f Meeting, 4-7 February

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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] 11th KAGRA f2f Meeting, 4-7 February LAL parameter estimation(PE) pipeline

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11th KAGRA f2f Meeting, 4-7 February waveform library [LALSimulation]

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LALInference/src/.. LALInference.h LALInferenceReadData.c LALInferecneTemplate.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; 11th KAGRA f2f Meeting, 4-7 February PE library [LALInference]

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LALInference/src/.. LALInference.h LALInferenceReadData.c LALInferecneTemplate.c 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 11th KAGRA f2f Meeting, 4-7 February PE library [LALInference]

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11th KAGRA f2f Meeting, 4-7 February PE library [LALInference] LALInference/src/.. LALInference.h LALInferenceReadData.c LALInferecneTemplate.c

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th KAGRA f2f Meeting, 4-7 February PE library [LALInference] LALInference/src/.. LALInference.h LALInferenceLikelihood.c LALInferecneTemplate.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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th KAGRA f2f Meeting, 4-7 February PE library [LALapps] LALapps/src/inspiral/posterior/.. LALInferenceMCMC.c LALInferenceMCMCSampler.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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th KAGRA f2f Meeting, 4-7 February PE library [LALapps] LALapps/src/inspiral/posterior/.. LALInferenceMCMC.c LALInferenceMCMCSampler.c LALInferenceMCMCSampler.c -> Bayesian Followup, MCMC algorithm PTMCMCAlgorithm() PTMCMCOneStep() -> Metropolis-Hasting algorithm implemented

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th KAGRA f2f Meeting, 4-7 February basic functions, libraries lal/FrequencySeries.h -> dataStructure lal/LALDatatypes.h ->Primitive datatypes Aggregate datatypes Store arbitrarily large sets or collections of primitive datatypes. aggregate datatypes are defines Structured datatypes : embed primitive and aggregate datatypes inside structures that define their physical meaning. 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 th KAGRA f2f Meeting, 4-7 February 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 11th KAGRA f2f Meeting, 4-7 February

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