A nonparametric empirical Bayes framework for large-scale multiple testing

We propose a exible and identi able version of the two-groups model, moti- vated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. We use a computationally e cient predictive recursion marginal likelihood procedure to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonpara- metric empirical Bayes testing procedure, which we call PRtest, based on thresh- olding the estimated local false discovery rates. Simulations and real-data examples demonstrate that, compared to existing approaches, PRtest's careful handling of the non-null density can give a much better t in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.