A New Calibrated Bayesian Internal Goodness-of-Fit Method: Sampled Posterior p-Values as Simple and General p-Values That Allow Double Use of the Data

Frédéric Gosselin

PLOS ONE, 2011, vol. 6, issue 3, 1-10

Abstract: Background: Recent approaches mixing frequentist principles with Bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of Bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function. Methodology/Principal Findings: We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution. Conclusions/Significance: These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0014770

DOI: 10.1371/journal.pone.0014770

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