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On the conservativeness of posterior predictive p-values

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  • Dahl, Fredrik Andreas

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.

Suggested Citation

  • Dahl, Fredrik Andreas, 2006. "On the conservativeness of posterior predictive p-values," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1170-1174, June.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:11:p:1170-1174
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    1. Hjort, Nils Lid & Dahl, Fredrik A. & Steinbakk, Gunnhildur Hognadottir, 2006. "Post-Processing Posterior Predictive p Values," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1157-1174, September.
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    Cited by:

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