  The analysis of large-scale datasets, especially in biomedical contexts,
frequently involves a principled screening of multiple hypotheses. The
celebrated two-group model jointly models the distribution of the test
statistics with mixtures of two competing densities, the null and the
alternative distributions. We investigate the use of weighted densities and, in
particular, non-local densities as working alternative distributions, to
enforce separation from the null and thus refine the screening procedure. We
show how these weighted alternatives improve various operating characteristics,
such as the Bayesian False Discovery rate, of the resulting tests for a fixed
mixture proportion with respect to a local, unweighted likelihood approach.
Parametric and nonparametric model specifications are proposed, along with
efficient samplers for posterior inference. By means of a simulation study, we
exhibit how our model compares with both well-established and state-of-the-art
alternatives in terms of various operating characteristics. Finally, to
illustrate the versatility of our method, we conduct three differential
expression analyses with publicly-available datasets from genomic studies of
heterogeneous nature.
