Bayesian semiparametric power spectral density estimation with applications in gravitational wave data analysis

TL;DR

This paper introduces a Bayesian semiparametric method for estimating the power spectral density in gravitational wave data, addressing non-stationarity and model misspecification to improve inference accuracy.

Contribution

It develops a novel Bayesian semiparametric approach using Bernstein polynomial priors and Dirichlet processes for PSD estimation in GW data analysis.

Findings

Effective PSD estimation in simulated GW data.

Improved handling of non-stationary noise.

Potential for more accurate GW signal reconstruction.

Abstract

The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data often depart from these assumptions, and misspecified parametric models of the PSD could result in misleading inferences. We propose a Bayesian semiparametric approach to improve this. We use a nonparametric Bernstein polynomial prior on the PSD, with weights attained via a Dirichlet process distribution, and update this using the Whittle likelihood. Posterior samples are obtained using a blocked Metropolis-within-Gibbs sampler. We simultaneously estimate the reconstruction parameters of a rotating core collapse supernova GW burst that has been embedded in simulated Advanced LIGO noise. We also discuss an approach to deal with non-stationary data by breaking longer data streams into smaller and locally stationary components.