Detecting non-Gaussian gravitational wave backgrounds: A unified framework

We describe a novel approach to the detection and parameter estimation of a non-Gaussian stochastic background of gravitational waves. The method is based on the determination of relevant statistical parameters using importance sampling. We show that it is possible to improve the Gaussian detection statistics by simulating realizations of the expected signal for a given model. While computationally expensive, our method improves the detection performance, leveraging the prior knowledge on the expected signal, and can be used in a natural way to extract physical information about the background. We present the basic principles of our approach, characterize the detection statistic performances in a simplified context, and discuss possible applications to the detection of some astrophysical foregrounds. We argue that the proposed approach, complementarily to the ones available in literature might be used to detect suitable astrophysical foregrounds by currently operating and future gravitational wave detectors.