Weakly parametric approach to stochastic background inference in LISA

Detecting stochastic gravitational wave backgrounds (SGWBs) with the Laser Interferometer Space Antenna (LISA) is one of the mission's scientific objectives. Disentangling SGWBs of astrophysical and cosmological origin is a challenging task, further complicated by the noise level uncertainties. In this study, we present a Bayesian methodology for inferring SGWBs, drawing inspiration from Gaussian stochastic processes. We assess the effectiveness of this approach for signals with unknown spectral shapes by systematically exploring the model hyperparameters---a preliminary step toward a more efficient transdimensional exploration. To validate our method, we apply it to a representative astrophysical scenario: the inference of the astrophysical background of extreme mass ratio inspirals, as recently estimated F. Pozzoli et al., Phys. Rev. D 108, 103039 (2023). Our findings indicate that the algorithm is capable of recovering the injected signal even with uninformative priors, simultaneously providing an estimate of the noise level.