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.
@article{arxiv.2412.10468,
title = {Is your stochastic signal really detectable?},
author = {Federico Pozzoli and Jonathan Gair and Riccardo Buscicchio and Lorenzo Speri},
journal= {arXiv preprint arXiv:2412.10468},
year = {2025}
}