A nonparametric empirical Bayes framework for large-scale multiple testing

TL;DR

This paper introduces PRtest, a nonparametric empirical Bayes method for large-scale multiple testing that improves tail fit and decision accuracy by modeling the non-null distribution flexibly.

Contribution

It develops a novel nonparametric empirical Bayes framework with an efficient estimation procedure, enhancing tail modeling and false discovery rate control in multiple testing.

Findings

PRtest provides better tail fit than existing methods.

Simulation studies show improved false discovery rate control.

Real data applications demonstrate more realistic conclusions.

Abstract

We propose 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. We use a computationally efficient predictive recursion marginal likelihood procedure to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonparametric empirical Bayes testing procedure, which we call 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.