Improving Parameter Estimation Efficiency for Advanced Detector Data Analysis of Compact Binary Coalescence

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

J.M. Bell, J. Veitch Improving CBC Parameter Estimation Efficiency 1 / 20



Gravitational WavesParameter EstimationNested SamplingMotivation

Gravitational Waves





Gravitational WavesFrom Compact Binary Coalescence





Parameter EstimationDoing the Physics!

I 2 MassesI TimeI Sky positionI DistanceI 2 Orientation AnglesI 6 Spin Components





Parameter EstimationA Bayesian Algorithm

Nested Sampling


Dropbox/IREU2013/FinalPresentation/nestedsampling.mp4




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




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.





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





Parallelization ResultsChirp Mass Cumulative Distributions

Factors of 1024 Factors of 256





Parallelization ResultsAccuracy and Efficiency

Posterior Samples

Nlive

Computational Time (s)

Nlive





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





Switching Gears

Time Domain to Frequency DomainF vs. T function





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





Variable Resolution MethodDetermining the Sampling Rate





Variable Resolution MethodA Broken Waveform





Variable Resolution ResultsAccuracy

Bands % Match1 99.99972 99.95413 99.75894 99.53515 99.3865





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





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




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




Summary and Outlook


Science

Improving Parameter Estimation Efficiency for Advanced Detector Data Analysis of Compact Binary Coalescence