A Nonparametric Empirical Bayes Framework for Large-Scale Multiple Testing

In this talk I will present a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. A computationally efficient predictive recursion marginal likelihood procedure is used to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonparametric empirical Bayes testing procedure, called PRtest, based on thresholding 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 fit in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.

(This is joint work with Professor Surya T. Tokdar at Duke University.)