A bayesian perspective on the bonferroni adjustment

Peter H. Westfall, Wesley O. Johnson, Jessica M. Utts

Research output: Contribution to journalArticlepeer-review

149 Scopus citations


Bayes/frequentist correspondences between the p-value and the posterior probability of the null hypothesis have been studied in univariate hypothesis testing situations. This paper extends these comparisons to multiple testing and in particular to the Bonferroni multiple testing method, in which p-values are adjusted by multiplying by k, the number of tests considered. In the Bayesian setting, prior assessments may need to be adjusted to account for multiple hypotheses, resulting in corresponding adjustments to the posterior probabilities. Conditions are given for which the adjusted posterior probabilities roughly correspond to Bonferroni adjusted p-values.

Original languageEnglish
Pages (from-to)419-427
Number of pages9
Issue number2
StatePublished - 1997


  • Adjusted p-value
  • Bayes factor
  • Multiple testing
  • Multiplicity adjustment
  • Simultaneous inference


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