An empirical Bayes mixture method for effect size and false discovery rate estimation

TL;DR

This paper introduces an empirical Bayes mixture model for joint effect size and false discovery rate estimation tailored for exponential family data, outperforming existing methods and enabling flexible, interpretable analysis.

Contribution

It presents a novel empirical Bayes mixture approach that estimates effect sizes and false discovery rates simultaneously, including an empirical null, for exponential family data.

Findings

Outperforms existing methods in normal data simulations.

Nearly achieves Bayes error for effect size estimation.

Provides a flexible, interpretable modeling framework.

Abstract

Many statistical problems involve data from thousands of parallel cases. Each case has some associated effect size, and most cases will have no effect. It is often important to estimate the effect size and the local or tail-area false discovery rate for each case. Most current methods do this separately, and most are designed for normal data. This paper uses an empirical Bayes mixture model approach to estimate both quantities together for exponential family data. The proposed method yields simple, interpretable models that can still be used nonparametrically. It can also estimate an empirical null and incorporate it fully into the model. The method outperforms existing effect size and false discovery rate estimation procedures in normal data simulations; it nearly acheives the Bayes error for effect size estimation. The method is implemented in an R package (mixfdr), freely available from CRAN.