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：03
出版社：Indian Statistical Institute
摘要：It is well-known that classical $p$-values sometimes behave incoherently for testing hypotheses in the sense that, when $\Theta_0\subset\Theta'_0,$ the support given to $\Theta_0$ is greater than or equal to the support given to $\Theta'_0.$. This problem is also found for posterior predictive $p$-values (a Bayesian-motivated alternative to classical $p$-values). In this paper, it is proved that, under some conditions, the posterior predictive $p$-value based on the posterior odds is coherent, showing that the choice of a suitable discrepancy variable is crucial.
