LAUSR

ABSTRACT When assessing the compatibility of an assumed model and the observed data, one popular method is the posterior predictive p-value (ppp). However, the posterior predictive p-values typically do not have uniform distributions and tend to be conservative when detecting the misfit of the assumed model. In this paper, we consider a calibrated p-value which is initially proposed in Hjort et al. [Post-processing posterior predictive p-values. J Am Stat Assoc. 2006;1011157–1174]. We further explore its theoretical properties by proving the asymptotic uniformity of the calibrated p-value under some mild conditions. For testing hypotheses under local Pitman alternatives, we investigate its power performance in the asymptotic sense. Theoretical analysis and simulation results show that the calibrated p-value enjoys some desirable properties and is superior to the original posterior predictive p-values.