A weakly-parametric approach to stochastic background inference in LISA

Abstract: Detecting stochastic gravitational wave backgrounds (SGWBs) with The Laser Interferometer Space Antenna (LISA) is among the mission science objectives. Disentangling SGWBs of astrophysical and cosmological origin is a challenging task, further complicated by the noise level uncertainties. In this study, we introduce a Bayesian methodology to infer upon SGWBs, taking inspiration from Gaussian stochastic processes. We investigate the suitability of the approach for signal of unknown spectral shape. We do by discretely exploring the model hyperparameters, a first step towards a more efficient transdimensional exploration. We apply the proposed method to a representative astrophysical scenario: the inference on the astrophysical foreground of Extreme Mass Ratio Inspirals, recently estimated in~\cite{Pozzoli2023}. We find the algorithm to be capable of recovering the injected signal even with large priors, while simultaneously providing estimate of the noise level.