期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2003
卷号：65
期号：01
页码：158--178
出版社：Indian Statistical Institute
摘要：In a hypothesis testing problem, the classical $p$-values are often perceived as measurements of the degree of surprise in the data, relative to a hypothesized model. The classical $p$-values commonly provide a basis for rejection of a hypothesis or a model. In this paper, we develop prior predictive and posterior predictive $p$-values for one sided hypothesis testing for location parameter problems. We show that for many classes of prior distributions, the infimum of the prior predictive and posterior predictive $p$-values are equal to the classical $p$-value, for very general classes of distributions. The results are in spirit similar to that in Casella and Berger (1987) in terms of reconciliation of Bayesian and frequentist evidence. The results are used through many examples relating to the one sided testing problem for location parameter.
关键词：Bayesian $p$-values, posterior probability, predictive distribution, prior distribution
