On spike and slab empirical Bayes multiple testing

TL;DR

This paper demonstrates that empirical Bayes spike and slab posterior distributions can effectively control the false discovery rate in sparse Gaussian models, providing a theoretical validation for these methods in multiple testing.

Contribution

It establishes a connection between empirical Bayes posteriors and FDR control, offering a theoretical validation in the context of sparse Gaussian models.

Findings

Empirical Bayes spike and slab methods control FDR under sparsity.

Theoretical validation of empirical Bayes in multiple testing.

Numerical experiments support the theoretical results.

Abstract

This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model, this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.