A family of Bayes multiple testing procedures

Arthur Cohen, H. B. Sackrowitz, Minya Xu, Steven Buyske

Research output: Contribution to journalArticlepeer-review

Abstract

Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the Benjamini-Hochberg step-up procedure for controlling false discovery rate as a baseline for conservativeness, we choose the tuning parameters to compromise between the operating characteristics of that procedure and a less conservative procedure that focuses on alternatives that a priori might be considered likely or meaningful. The Bayes procedures do not have the theoretical and practical shortcomings of the popular stepwise procedures. In terms of the number of mistakes, simulations for two examples indicate that over a large segment of the parameter space, the Bayes procedure is preferable to the step-up procedure. Another desirable feature of the procedures is that they are computationally feasible for any number of hypotheses.

Original languageEnglish (US)
Pages (from-to)295-305
Number of pages11
JournalBiometrika
Volume95
Issue number2
DOIs
StatePublished - Jun 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • False discovery rate
  • Familywise error rate
  • Genomics
  • Noncentral chi-squared density
  • Noncentral t density
  • Step-down procedure
  • Step-up procedure

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