P-values have been the focus of considerable criticism based on various
considerations. Still, the P-value represents one of the most commonly used
statistical tools. When assessing the suitability of a single hypothesized
distribution, it is not clear that there is a better choice for a measure of
surprise. This paper is concerned with the definition of appropriate
model-based P-values for model checking.Comment: Published in at http://dx.doi.org/10.1214/09-AOS727 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org