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

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

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

Computational Time (s)

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

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

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

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