On spike and slab empirical Bayes multiple testing
Ismaël Castillo, Étienne Roquain
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.
Topics & Concepts
Frequentist inferenceBayes' theoremFalse discovery rateSpike (software development)Prior probabilityBayes factorComputer sciencePosterior probabilityContext (archaeology)Bayesian probabilitySequence (biology)EconometricsStatisticsMathematicsMachine learningArtificial intelligenceBayesian inferenceGeologyBiologyGeneticsSoftware engineeringPaleontologyGeneBiochemistryStatistical Methods in Clinical TrialsStatistical Methods and Bayesian InferenceOptimal Experimental Design Methods