improving parameter estimation efficiency for advanced detector data analysis of compact binary...
TRANSCRIPT
IntroductionParallelization
Variable ResolutionSummary
Improving Parameter Estimation Efficiencyfor Advanced Detector Data Analysis
of Compact Binary Coalescence
J. M. Bell1 2 J. Veitch2 3
1Millsaps College
2Gravitational PhysicsNIKHEF
3Department of PhysicsUniversity of Birmingham Physics
University of Florida IREU in Gravitational Physics
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IntroductionParallelization
Variable ResolutionSummary
Gravitational WavesParameter EstimationNested SamplingMotivation
Gravitational Waves
J.M. Bell, J. Veitch Improving CBC Parameter Estimation Efficiency 2 / 20
IntroductionParallelization
Variable ResolutionSummary
Gravitational WavesParameter EstimationNested SamplingMotivation
Gravitational WavesFrom Compact Binary Coalescence
J.M. Bell, J. Veitch Improving CBC Parameter Estimation Efficiency 3 / 20
IntroductionParallelization
Variable ResolutionSummary
Gravitational WavesParameter EstimationNested SamplingMotivation
Parameter EstimationDoing the Physics!
I 2 MassesI TimeI Sky positionI DistanceI 2 Orientation AnglesI 6 Spin Components
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IntroductionParallelization
Variable ResolutionSummary
Gravitational WavesParameter EstimationNested SamplingMotivation
Parameter EstimationA Bayesian Algorithm
Nested Sampling
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IntroductionParallelization
Variable ResolutionSummary
Gravitational WavesParameter EstimationNested SamplingMotivation
Motivation
I The Problem:Data analysis via Nested Sampling takes time
I The Solution:Improving the efficiency of Nested Sampling
I ParallelizationI Multiple Bandwidth Analysis
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Parallelization
I Nested sampling converges on the maximum likelihoodI faster with the use of fewer live pointsI more accurately with the use of more live points
I Goals:I to reduce overall computational time while maintaining
sufficient accuracyI to optimize this procedure by finding the most effective
range of live points.
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
ParallelizationMethod
1 Run multiple instances in parallel with different NliveI 1 @ 1024I 2 @ 512I 4 @ 256
...I 64 @ 16
2 Recombine the results weighted by their parameterestimates
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Parallelization ResultsChirp Mass Cumulative Distributions
Factors of 1024 Factors of 256
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Parallelization ResultsAccuracy and Efficiency
Posterior Samples
Nlive
Computational Time (s)
Nlive
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
ParallelizationConclusions
I Parallelization can reduce computational time arbitrarilyI Reducing Nlive by 50% returns 75% of the posterior
samples
I The optimal range for Nlive is 200 to 256I The total Nlive across instances should be over 1000
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Switching Gears
Time Domain to Frequency DomainF vs. T function
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Multi-bandwidth Analysis
I Resolution is related to the number of samples in aninterval
I high resolution is redundantI low resolution is efficient
I Plan:I to downsample the frequency domain waveform according
to an optimized function based on the Nyquist timeI Goals:
I to exploit the monochromatic, low frequency nature of theearly waveform
I to focus computational resources on the more complexregion near the merger
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Variable Resolution MethodDetermining the Sampling Rate
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Variable Resolution MethodA Broken Waveform
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Variable Resolution ResultsAccuracy
Bands % Match1 99.99972 99.95413 99.75894 99.53515 99.3865
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Variable Resolution ResultsEfficiency
Bands d+hh:mm:ss1 ≈ 4+09:00:002 3+16:28:543 2+23:22:124 2+18:19:395 2+17:30:19
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IntroductionParallelization
Variable ResolutionSummary
OverviewMethodResultsConclusions
Variable Resolution Conclusions
I Variable Resolution analyses are feasible for parameterestimation
I A computation requiring roughly 50% of the time retainsover 99% of the accuracy
I Other methods of interpolation could lead to greateraccuracy
I Further work needed to eliminate remaining issues
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IntroductionParallelization
Variable ResolutionSummary
Summary and Outlook
Summary and Outlook
I Parallelization and Variable Resolution are viable means ofreducing computational time
I What lies ahead?I Optimization of the multiband algorithmI Simultaneous testing of both approachesI Implementation in the time domain
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IntroductionParallelization
Variable ResolutionSummary
Summary and Outlook
J.M. Bell, J. Veitch Improving CBC Parameter Estimation Efficiency 20 / 20