Reconciling bayesian and frequentist evidence in the one-sided testing problem

George Casella, Roger L. Berger

Research output: Contribution to journalArticlepeer-review

244 Scopus citations

Abstract

For the one-sided hypothesis testing problem it is shown that it is possible to reconcile Bayesian evidence against H0, expressed in terms of the posterior probability that H0is true, with frequentist evidence against H0, expressed in terms of the p value. In fact, for many classes of prior distributions it is shown that the infimum of the Bayesian posterior probability of H0is equal to the p value; in other cases the infimum is less than the p value. The results are in contrast to recent work of Berger and Sellke (1987) in the two-sided (point null) case, where it was found that the p value is much smaller than the Bayesian infimum. Some comments on the point null problem are also given.

Original languageEnglish (US)
Pages (from-to)106-111
Number of pages6
JournalJournal of the American Statistical Association
Volume82
Issue number397
DOIs
StatePublished - Mar 1987

Keywords

  • Posterior probability
  • Prior distribution
  • p Value

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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