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P Values for Composite Null Models

M. J. Bayarri and James O. Berger
Journal of the American Statistical Association
Vol. 95, No. 452 (Dec., 2000), pp. 1127-1142
DOI: 10.2307/2669749
Stable URL: http://www.jstor.org/stable/2669749
Page Count: 16
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P Values for Composite Null Models
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Abstract

The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters, p values are not uniquely defined. The proposals for computing a p value in such a situation include the plug-in and similar p values on the frequentist side, and the predictive and posterior predictive p values on the Bayesian side. We propose two alternatives, the conditional predictive p value and the partial posterior predictive p value, and indicate their advantages from both Bayesian and frequentist perspectives.

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