Characterization of non-Gaussian stochastic signals with heavier-tailed likelihoods

Future gravitational wave observatories will give us the opportunity to search for stochastic signals of astrophysical or even cosmological origins. However, parameter estimation and search will be challenging, mostly due to the overlap of multiple signal components, as well as the potentially partially unknown properties of the instrumental noise. In this work, we propose a robust statistical framework based on heavier-tailed likelihoods for the characterization of stochastic gravitational wave signals. In particular, we use the symmetric hyperbolic likelihood, which allows us to probe the signal spectral properties and simultaneously test for any departures from Gaussianity. We demonstrate this methodology with synthetic data from the future LISA mission, where we estimate the potential non-Gaussianities induced by the unresolved ultracompact Galactic binaries.