On spike and slab empirical Bayes multiple testing

Ismael Castillo (1) , Etienne Roquain (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Mots clés: sparsity; False discovery rate; Frequentist properties of Bayesian procedures; multiple testing

Domaines: Théorie [stat.TH]

Ismael Castillo, Etienne Roquain. On spike and slab empirical Bayes multiple testing. 2018. ⟨hal-01855417⟩