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Computational techniques for parameter estimation of gravitational wave signals

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Abstract Since the very first detection of gravitational waves from the coalescence of two black holes in 2015, Bayesian statistical methods have been routinely applied by LIGO and Virgo to extract the signal out of noisy interferometric measurements, obtain point estimates of the physical parameters responsible for producing the signal, and rigorously quantify their uncertainties. Different computational techniques have been devised depending on the source of the gravitational radiation and the gravitational waveform model used. Prominent sources of gravitational waves are binary black hole or neutron star mergers, the only objects that have been observed by detectors to date. But also gravitational waves from core‐collapse supernovae, rapidly rotating neutron stars, and the stochastic gravitational‐wave background are in the sensitivity band of the ground‐based interferometers and expected to be observable in future observation runs. As nonlinearities of the complex waveforms and the high‐dimensional parameter spaces preclude analytic evaluation of the posterior distribution, posterior inference for all these sources relies on computer‐intensive simulation techniques such as Markov chain Monte Carlo methods. A review of state‐of‐the‐art Bayesian statistical parameter estimation methods will be given for researchers in this cross‐disciplinary area of gravitational wave data analysis. This article is categorized under: Applications of Computational Statistics > Signal and Image Processing and Coding Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical Models > Time Series Models
The Advanced LIGO and Advanced Virgo sensitivity curves. These are typical of the best sensitivities of the detectors during their second observational run (B. Abbott, Abbott, Abbott, Abraham, et al., 2019d). Source: LIGO Scientific Collaboration
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Estimated log spectral density for a 1 s segment of Advanced LIGO S6 data. The posterior median log spectral density estimate using the corrected likelihood with an AR(35) working model (solid black), pointwise 90% credible region (shaded red), and uniform 90% credible region (shaded violet) are overlaid with the log periodogram (gray; Kirch et al., 2019)
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Reconstructed CCSN signal from the Dimmelmeier et al. (2008) waveform catalog using a transdimensional PCR model. The true signal (solid black) and model‐averaged reconstruction (dashed blue) are overlaid with the model‐averaged 90% credible region (shaded pink)
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The detector strain measurements of GW150914 (B. Abbott et al., 2016c) observed by the LIGO Hanford (H1, top) and Livingston (L1, bottom) detectors in gray. Times are shown relative to September 14, 2015, at 09:50:45 UTC. The cyan curve is the estimated signal using the IMRPhenom and EOBNR waveform templates, the blue curve a signal reconstruction based on BayesWave. Source: B. Abbott et al. (2016d)
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Simulated gravitational wave signals with different waveforms: a compact binary inspiral, core‐collapse supernova, continuous‐wave, and stochastic gravitational‐wave signal. Credit: A. Stuver, LIGO Scientific Collaboration (Stuver, 2020)
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Statistical Models > Time Series Models
Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
Applications of Computational Statistics > Signal and Image Processing and Coding

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