Bayesian hypotheses testing using posterior density ratios

Sanjib Basu

Statistics & Probability Letters, 1996, vol. 30, issue 1, 79-86

Abstract: The posterior density ratio sup[theta][epsilon]Ho [pi]([theta]data)/sup[theta][epsilon]H1 [pi]([theta]data) is proposed as a new criterion for Bayesian hypothesis testing. The performances of the posterior density ratio and the posterior probability of Ho are compared in point null hypothesis, precise hypothesis and one sided hypothesis tests. It is found that the likelihood ratio and the lower bound of the posterior density ratio over a scale mixture class of priors match in point null hypothesis testing. They, however, do not match in one sided testing.

Keywords: Bayes; factor; Hypothesis; test; Likelihood; ratio; Posterior; Robust; Bayes (search for similar items in EconPapers)
Date: 1996
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