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.
"On spike and slab empirical Bayes multiple testing." Ann. Statist. 48 (5) 2548 - 2574, October 2020. https://doi.org/10.1214/19-AOS1897