Noise spectral estimation methods and their impact on gravitational wave measurement of compact binary mergers

Abstract

Estimating the parameters of gravitational wave signals detected by ground-based detectors requires an understanding of the properties of the detectors' noise. In particular, the most commonly used likelihood function for gravitational wave data analysis assumes that the noise is Gaussian, stationary, and of known frequency-dependent variance. The variance of the colored Gaussian noise is used as a whitening filter on the data before computation of the likelihood function. In practice the noise variance is not known and it evolves over timescales of dozens of seconds to minutes. We study two methods for estimating this whitening filter for ground-based gravitational wave detectors with the goal of performing parameter estimation studies. The first method uses large amounts of data separated from the specific segment we wish to analyze and computes the power spectral density of the noise through the mean-median Welch method. The second method uses the same data segment as the parameter estimation analysis, which potentially includes a gravitational wave signal, and obtains the whitening filter through a fit of the power spectrum of the data in terms of a sum of splines and Lorentzians. We compare these two methods and argue that the latter is more reliable for gravitational wave parameter estimation. arXiv:1907.06540v1 [gr-qc]

GW190412: Observation of a binary-black-hole coalescence with asymmetric masses

“…RIFT [103,104] was also used to check consistency of the intrinsic parameters and for corroborating the Bayes factors that are presented below. The power spectral density (PSD) of the noise that enters the likelihood calculation is estimated from the data using BayesWave [105,106]. The lowfrequency cutoff for the likelihood integration is set to 20 Hz, and the prior distributions we use are described in Appendix B 1 of [7].…”

Bayesian inference for compact binary coalescences with bilby: validation and application to the first LIGO–Virgo gravitational-wave transient catalogue

“…In order to avoid including any signal in the PSD calculation, bilby_pipe uses a stretch of data preceding the analysis segment. Following Veitch et al (2015) and Chatziioannou et al (2019), we use data stretches of length min(32T, 1024 s) by default, although both of these values can be altered by the user. The upper limit of 1024 s is required because the PSD of gravitational-wave detectors is non-stationary over long time-periods (Chatziioannou et al 2019).…”

“…Following Veitch et al (2015) and Chatziioannou et al (2019), we use data stretches of length min(32T, 1024 s) by default, although both of these values can be altered by the user. The upper limit of 1024 s is required because the PSD of gravitational-wave detectors is non-stationary over long time-periods (Chatziioannou et al 2019). To further mitigate this issue, the data is divided into segments of length T , with each segment overlapping 50% of the previous segment; this allows a shorter total stretch of data to be used to calculate the PSD.…”

BayesWave analysis pipeline in the era of gravitational wave observations

“…Again, a transdimensional MCMC algorithm is used to marginalize over the number of Lorentzians used in the fit. BayesLine has been shown to outperform periodogram-based approaches for spectral estimation in LIGO-Virgo data because it only assumes the noise to be stationary over the interval of data being analyzed, as opposed to the interval of data needed for the periodogram [6].…”