1. KAGALI PE code development
Hyung Won Lee, Inje University, 24 June 2016
coll. With Jeongcho Kim(Inje U.), Chunglee Kim(SNU)
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

2. Contents Motivation Parameter Estimation with Bayesian Inference
Implementation in LALSuite
Strategy for KAGALI
Development for KAGALI
Progress from the last
Discussions
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

3. Motivation Implement MCMC PE for KAGALI Based on LALSuite
Minimum full functionality for MCMC
Parallel tempered
Improvement as many as possible from LALSuite
Modularize as much as possible for easy maintenance and readable
Ready for iKAGRA data analysis
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

4. Parameter Estimation with Bayesian inference
℘ 𝜃 𝑥 = ℘ 𝜃, 𝑥 ℘ 𝑥 = ℘(𝑥|𝜃)℘ 𝜃 ℘(𝑥|𝜃)℘ 𝜃 𝑑𝜃
℘ 𝜃,𝑥 =℘ 𝑥 𝜃 ℘ 𝜃 =℘ 𝜃 𝑥 ℘ 𝑥
𝜃 : unobservable model parameters
𝑥 : observable data
℘ 𝜃,𝑥 : Joint probability observing data 𝑥 with model parameter 𝜃
℘ 𝑥 𝜃 ∝𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛
Metropolis-Hasting Algorithm, ~ samples
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

5. Parameter Estimation with Bayesian inference
MCMC Samples
MCMC Samples
PTMCMCOutput.00
PTMCMCOutput.nn
Post Process
Post Process
cbcByesPostProc.py
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

6. Waveform Templates There are many waveform templates
Concentrate taylorF2 with
Amplitude correction up to 2.5 PN
Effect of eccentricity up to 3.0 PN
TaylorT2 can deal with CBC inspirals when there is a BH spin that is aligned to the orbital angular momentum.
SpinTaylorT4 is one of the most comprehensive inspiral waveform model used by the LIGO-Virgo collaboration. This can deal with precessing CBC inspirals with two spins.
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

7. Likelihood Calculation
ℒ(𝑠|𝜃)∝exp −2 0 ∞ 𝑠 𝑓 − ℎ (𝜃,𝑓) 2 𝑆 𝑛 (𝑓) 𝑑𝑓
Gaussian noise assumption
℘ 𝑥 𝜃 = ℒ(𝑠|𝜃)
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

8. MCMC Process Parallel Tempering Accept next state with probability
𝑟= ℘(𝑥| 𝜃 2 ) 1/𝑇 ℘ 𝜃 ℘(𝑥| 𝜃 1 ) 1/𝑇 ℘ 𝜃 1
Metropolis-Hasting sampling
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

9. Parallel Tempering Use few chains with different temperature
Use likelihood ℒ 𝑠 𝜃 1 𝑇 , 𝑇>1
𝑇 𝑚𝑎𝑥 = 𝑁𝑒𝑡𝑤𝑜𝑟𝑘 𝑆𝑁𝑅 2 𝑛 𝑝𝑎𝑟
Improve convergence and mixing
The higher temperature, the smoother distribution
𝑇>1
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

10. Implementation in lalsuite
LAL MCMC Pipeline
Directory structure of lalsuite
Basic entities of LALSuite
LAL applications
Likelihood, proposal and prior functions
Simulation related functions and waveforms
Post Processing python script
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

11. LAL MCMC Pipeline Start Initialization MPI synchronize PT MCMC
Clearance
End
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

12. main LALInferenceInitRunState() LALInferenceInjectSignal()
LALInferenceApplyCalibrationErrors()
init_ptmcmc()
LALInferenceInitCBCPrior()
LALInferenceInitLikelihood()
LALInferenceDrawThreads()
runState->algorithm
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

13. InitRunState() Makoto & Takuji, 2 19937 −1≈ 10 6000 2016-06-24
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

14. LALInferenceInjectInspiralSignal()
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

15. LALInferenceApplyCalibrationErrors()
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16. init_ptmcmc()
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

17. LALInferenceInspiralPrior()
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18. PTMCMCAlgorithm()
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

19. Template LALInferenceTemplateXLALSimInspiralChooseWaveform 2016-06-24
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

20. Strategy for KAGALI Base on LALSuite for many functions
Modularize if possible
Use structures
Command parameters(KGLProcessParamsTable)
IFO information(KGLInferenceIFOData)
Waveform parameters(KGLWaveformModelParams)
MCMC status(KGLInferenceRunState)
Simulation parameters
Use simple text file for injections
Ready for iKAGRA data(hope, to be done)
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

21. Development for KAGALI
Use a new branch “mcmc” for development
Library and application directory are separated (version 4)
root/kagali/inference/src
root/kagali/kglcommon/clock/src
root/kagali/kglcommon/detector/src
root/kagali/kglcommon/std/src
root/kagali/waveform/src
root/kagaliapps/cbc/mpisrc
Cloned on KISTI and local Ubuntu server
Build and run on both systems
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

22. Main features
Use a unique union structure for waveform parameters (KGLWaveformModelParams)
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

23. Structures KGLInferenceIFOData KGLWaveformModelParamsValue
KGLProcessParamsTable
KGLInferenceRunState
KGLWaveformModelParams
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

24.
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

25.
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

26. Development for KAGALI
kagali/inference/src
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

27. Development for KAGALI
kagali/kglcommon/clock/src
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

28. Development for KAGALI
kagali/kglcommon/detector/src
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

29. Development for KAGALI
kagali/kglcommon/std/src
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

30. Development for KAGALI
kagali/waveform/src
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

31. Development for KAGALI
kagaliapps/cbc/mpisrc
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

32. KGLProcessParamsTable.h.in 2016-06-24
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

33. KGLProcessParamsTable.h.in KGLProcessParamsPair KGLProcessParamsTable
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

34. KGLCommandUtils.c
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35. KGLInferenceMCMC.c
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36. inferenceMCMC.c
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37. inferenceMCMC.c
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

38. Makefile.am
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

39. build KAGALI
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

40. build script
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

41. build script(cont’d) 2016-06-24
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

42. Build results nohup ./build-branch.sh & 2016-06-24
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

43. Sample run
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

44. Sample run(con’d)
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45. Progress from the last Defines some structures
Waveform Parameters, Datetime, etc.
Implement basic placeholder functions
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

46. Discussions Basic data structures are ready
Basic program architecture fixed
Need to write source codes and hurry up
Hanyang, SNU
Seoul
Toyama
KISTI, NIMS
Daejeon
Pusan U.
Osaka
Gimhae
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI

47. Thanks
KAGALI PE code development, The 1st International Meeting on KAGRA, KISTI