On spike and slab empirical Bayes multiple testing
Ismaël Castillo, Étienne Roquain
The Annals of Statistics · 2020 · Volume 48 · Issue 5
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.
Keywords
62C12, 62G10, False discovery rate, Frequentist properties of Bayesian procedures, multiple testing, Sparsity
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