Likelihoods for Stochastic Gravitational Wave Background Data Analysis

TL;DR

This paper systematically examines the likelihood functions used in stochastic gravitational wave background data analysis, highlighting potential biases from Gaussian approximations and offering guidance for robust inference in various detector regimes.

Contribution

It introduces a hierarchy of likelihood approximations, analyzes their biases, and discusses strategies to improve SGWB parameter estimation accuracy.

Findings

Gaussian likelihood approximations can induce biases in parameter estimation.

Biases can exceed statistical uncertainties in space-based and pulsar-timing arrays.

Guidelines for segment duration and likelihood choice improve robustness of SGWB inference.

Abstract

We present a systematic study of likelihood functions used for Stochastic Gravitational Wave Background (SGWB) searches. By dividing the data into many short segments, one customarily takes advantage of the Central Limit Theorem to justify a Gaussian crosscorrelation likelihood. We show, with a hierarchy of ever more realistic examples, beginning with a single frequency bin and one detector, and then moving to two and three detectors with white and colored signal and noise, that approximating the exact Whittle likelihood by various Gaussian alternatives can induce systematic biases in the estimation of the SGWB parameters. We derive several approximations for the full likelihood and identify regimes where Gaussianity breaks down. We also discuss the possibility of conditioning the full likelihood on fiducial noise estimates to produce unbiased SGWB parameter estimation. We show that for some segment durations and bandwidths, particularly in space-based and pulsar-timing arrays, the bias can exceed the statistical uncertainty. Our results provide practical guidance for segment choice, likelihood selection, and data-compression strategies to ensure robust SGWB inference in current and next-generation gravitational wave detectors.