On the conservativeness of posterior predictive p-values

Fredrik Andreas Dahl

Statistics & Probability Letters, 2006, vol. 76, issue 11, 1170-1174

Abstract: Bayesian posterior predictive p-values (ppp) tend to be conservative, in the sense of low rejection probability under the prior distribution. It is well known that a ppp has the distribution of a conditional expectancy of a uniform (0,1) variable. We show that this does not imply a tail probability inequality P(ppp[less-than-or-equals, slant][alpha])[less-than-or-equals, slant][alpha], even when [alpha] tends to zero. In some special cases involving localization parameters, however, we show that ppp-values are in fact strictly conservative.

Date: 2006
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