Frequentist Properties of Bayesian Multiplicity Control for Multiple Testing of Normal Means

Sean Chang () and James O. Berger ()
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Sean Chang: Duke University
James O. Berger: Duke University

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 2, 310-329

Abstract: Abstract We consider the standard problem of multiple testing of normal means, obtaining Bayesian multiplicity control by assuming that the prior inclusion probability (the assumed equal prior probability that each mean is nonzero) is unknown and assigned a prior distribution. The asymptotic frequentist behavior of the Bayesian procedure is studied, as the number of tests grows. Studied quantities include the false positive probability, which is shown to go to zero asymptotically. The asymptotics of a Bayesian decision-theoretic approach are also presented.

Keywords: Multiple hypothesis testing; spike-and-slab prior; multiplicity control; false positive probability.; Primary 62C10; Secondary 62J15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13171-019-00192-1

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