Is your stochastic signal really detectable?

TL;DR

This paper introduces a Bayesian framework for detecting stochastic gravitational wave backgrounds that accounts for uncertainties in both the signal and noise, improving robustness over existing methods.

Contribution

It presents a formalism to compute the averaged Bayes factor considering instrumental noise and SGWB uncertainties, offering a more reliable detection criterion.

Findings

Developed a Bayesian sensitivity curve for LISA SGWB detection.

Incorporated uncertainties in both signal and noise into the detection formalism.

Provided a more realistic detection threshold compared to traditional methods.

Abstract

Separating a stochastic gravitational wave background (SGWB) from noise is a challenging statistical task. One approach to establishing a detection criterion for the SGWB is using Bayesian evidence. If the evidence ratio (Bayes factor) between models with and without the signal exceeds a certain threshold, the signal is considered detected. We present a formalism to compute the averaged Bayes factor, incorporating instrumental-noise and SGWB uncertainties. As an example, we consider the case of power-law-shaped SGWB in LISA and generate the corresponding Bayesian sensitivity curve. Unlike existing methods in the literature, which typically neglect uncertainties in both the signal and noise, our approach provides a reliable and realistic alternative. This flexible framework opens avenues for more robust stochastic gravitational wave background detection across gravitational-wave experiments.