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A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values
1Cemagref, UR EFNO, Nogent-sur-Vernisson, France. lfiorenza@senckenberg.de
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.
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