Abstract
This paper gives an exposition of the use of the posterior likelihood ratio for testing point null hypotheses in a fully Bayesian framework. Connections between the frequentist P-value and the posterior distribution of the likelihood ratio are used to interpret and calibrate P-values in a Bayesian context, and examples are given to show the use of simple posterior simulation methods to provide Bayesian tests of common hypotheses.
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Aitkin, M., Boys, R.J. & Chadwick, T. Bayesian point null hypothesis testing via the posterior likelihood ratio. Stat Comput 15, 217–230 (2005). https://doi.org/10.1007/s11222-005-1310-0
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DOI: https://doi.org/10.1007/s11222-005-1310-0