Open Access
October 2020 On spike and slab empirical Bayes multiple testing
Ismaël Castillo, Étienne Roquain
Ann. Statist. 48(5): 2548-2574 (October 2020). DOI: 10.1214/19-AOS1897


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.


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Ismaël Castillo. Étienne Roquain. "On spike and slab empirical Bayes multiple testing." Ann. Statist. 48 (5) 2548 - 2574, October 2020.


Received: 1 August 2018; Revised: 1 June 2019; Published: October 2020
First available in Project Euclid: 19 September 2020

MathSciNet: MR4152112
Digital Object Identifier: 10.1214/19-AOS1897

Primary: 62C12 , 62G10

Keywords: False discovery rate , Frequentist properties of Bayesian procedures , multiple testing , Sparsity

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 5 • October 2020
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