  We describe a novel approach to the detection and parameter estimation of a
non\textendash 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.
