Improved detection statistics for non Gaussian gravitational wave stochastic backgrounds

In a recent paper we described a novel approach to the detection and parameter estimation of a non\textendash Gaussian stochastic background of gravitational waves. We devised an inference procedure that uses signal realizations and importance sampling to weight integrals appearing in relevant statistical quantities. In particular, we constructed the associated detection statistics: in order to provide robustness against stationary noise uncertainties we proposed a subtraction procedure to remove terms with non--zero expectation values in absence of signal. We characterized the detector statistics performances, and observed that for low to moderate non-Gaussianities it is outperformed by established Gaussian inference schemes. In this work we propose a more careful, robust subtraction procedure: while still using the importance sampling scheme, it does not introduce performance penalties. We provide formal proof of its efficiency and, following closely the approach in our previous paper, we benchmark its performances on the same toy model: the proposed approach performs better than the Gaussian statistics everywhere in the model parameter space, therefore constituting a crucial addition to our framework.