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Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem
George Casella and Roger L. Berger
Journal of the American Statistical Association
Vol. 82, No. 397 (Mar., 1987), pp. 106-111
Stable URL: http://www.jstor.org/stable/2289130
Page Count: 6
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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 H0 is 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 H0 is 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.
Journal of the American Statistical Association © 1987 American Statistical Association