• gravitational waves
• stochastic background

We present an alternative approach for the detection of a non-Gaussian gravitational wave stochastic background, based on the likelihood ratio. This should lead to optimality according to the Neyman-Pearson lemma. In fact, while in the case of a Gaussian background it is well known that cross-correlating data from a network of interferometer gives optimal results in terms of detection probablity at fixed false alarm probability, this may not be the case for the non-Gaussian case.
We characterize the two approaches in a simple "toy" model, and from a comparison we find out that our optimal approach outperforms the cross-correlation statistic if a high enough level of non-Gaussianity of the signal distribution is present. In doing so, it is important to note that noise dominated terms should not be included in the statistics, since it is unlikely to estimate the noise budget of the interferometers in use with a precision of the order of the gravitational background.
For the proposed statistic, this problem can be avoided by manipulating the data set in an appropriate way, at the cost of introducing some noise.
However, we explore an alternative version in which we eliminate the dangerous terms directly from the expression of the statistic. As a results, the detection probability is further improved, especially for larger detector networks.
The given analysis gives promising results, which may be followed by a characterization on a more realistic model.