On a Bayesian P-value with the Coherence Property

Schervish(1996) and Lavine and Schervish(1999) have shown that the classical P-values and the Bayes factors fail to achieve the so-called coherence property, respectively. In this paper, we propose a new type of Bayesian P-value, namely the type LR Bayesian P-value, satisfying the coherence property. The proposed Bayesian P-values are very easy to use with since they are simple functions of likelihood ratio. Their performances are discussed and compared with those of other methods under several situations.