When is a gravitational-wave signal stochastic?

TL;DR

This paper explores how to classify gravitational-wave signals as stochastic or deterministic using Bayesian inference, providing a practical framework and analyzing different source population scenarios.

Contribution

It introduces a Bayesian model selection approach to distinguish stochastic from deterministic gravitational-wave signals and proposes a hybrid model that outperforms others.

Findings

Deterministic signals favored at low source numbers

Gaussian-stochastic signals favored at high source numbers

Hybrid model combining deterministic and Gaussian-stochastic components performs best

Abstract

We discuss the detection of gravitational-wave backgrounds in the context of Bayesian inference and suggest a practical definition of what it means for a signal to be considered stochastic---namely, that the Bayesian evidence favors a stochastic signal model over a deterministic signal model. A signal can further be classified as Gaussian-stochastic if a Gaussian signal model is favored. In our analysis we use Bayesian model selection to choose between several signal and noise models for simulated data consisting of uncorrelated Gaussian detector noise plus a superposition of sinusoidal signals from an astrophysical population of gravitational-wave sources. For simplicity, we consider co-located and co-aligned detectors with white detector noise, but the method can be extended to more realistic detector configurations and power spectra. The general trend we observe is that a deterministic model is favored for small source numbers, a non-Gaussian stochastic model is preferred for intermediate source numbers, and a Gaussian stochastic model is preferred for large source numbers. However, there is very large variation between individual signal realizations, leading to fuzzy boundaries between the three regimes. We find that a hybrid, trans-dimensional model comprised of a deterministic signal model for individual bright sources and a Gaussian-stochastic signal model for the remaining confusion background outperforms all other models in most instances.