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

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Listed:
  • Sean Chang

    (Duke University)

  • James O. Berger

    (Duke University)

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.

Suggested Citation

  • Sean Chang & James O. Berger, 2020. "Frequentist Properties of Bayesian Multiplicity Control for Multiple Testing of Normal Means," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 310-329, August.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00192-1
    DOI: 10.1007/s13171-019-00192-1
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    References listed on IDEAS

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    1. Michele Guindani & Peter Müller & Song Zhang, 2009. "A Bayesian discovery procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 905-925, November.
    2. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
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