Bayesian point null hypothesis testing via the posterior likelihood ratio

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.