Abstract
The posterior distribution of the likelihood is used to interpret the evidential meaning of P-values, posterior Bayes factors and Akaike's information criterion when comparing point null hypotheses with composite alternatives. Asymptotic arguments lead to simple re-calibrations of these criteria in terms of posterior tail probabilities of the likelihood ratio. (‘Prior’) Bayes factors cannot be calibrated in this way as they are model-specific.
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Aitkin, M. The calibration of P-values, posterior Bayes factors and the AIC from the posterior distribution of the likelihood. Statistics and Computing 7, 253–261 (1997). https://doi.org/10.1023/A:1018550505678
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DOI: https://doi.org/10.1023/A:1018550505678