# Assessing the detectability of a Stochastic Gravitational Wave Background with LISA, using an excess of power approach

## TL;DR

This paper introduces a rapid analytical method to evaluate the detectability of a stochastic gravitational wave background with LISA, focusing on Bayesian model comparison to determine detection bounds across frequencies.

## Contribution

It presents a novel analytic approach to assess the detectability of stochastic signals with LISA, enabling quick bounds calculation based on Bayesian analysis.

## Key findings

- Derived an explicit Bayes Factor expression for detection assessment.
- Provided a method to compute detectability bounds as a function of frequency.
- Facilitated rapid evaluation of stochastic background detectability for LISA.

## Abstract

The Laser Interferometer Space Antenna will be the first Gravitational Wave observatory in space. It is scheduled to fly in the early 2030's. LISA design predicts sensitivity levels that enable the detection a Stochastic Gravitational Wave Background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes Factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum.