A Semi-Parametric Approach to the Detection of Non-Gaussian Gravitational Wave Stochastic Backgrounds

TL;DR

This paper introduces a semi-parametric method using the Edgeworth expansion to detect non-Gaussian gravitational wave backgrounds, enabling estimation of higher-order distribution features to inform astrophysical models.

Contribution

It develops an explicit likelihood detection statistic for non-Gaussian signals and demonstrates the feasibility of estimating higher-order cumulants from data.

Findings

Likelihood detection statistic derived for non-Gaussian backgrounds

Fourth cumulant can be estimated with reasonable accuracy when signal-to-noise ratio > 0.01

Higher-order cumulants provide additional astrophysical constraints

Abstract

Using a semi-parametric approach based on the fourth-order Edgeworth expansion for the unknown signal distribution, we derive an explicit expression for the likelihood detection statistic in the presence of non-normally distributed gravitational wave stochastic backgrounds. Numerical likelihood maximization exercises based on Monte-Carlo simulations for a set of large tail symmetric non-Gaussian distributions suggest that the fourth cumulant of the signal distribution can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 0.01. The estimation of higher-order cumulants of the observed gravitational wave signal distribution is expected to provide additional constraints on astrophysical and cosmological models.