Default Bayes Factors for one-sided hypothesis testing

Abstract

Bayesian hypothesis testing for non-nested hypotheses various "default" Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing and expected intrinsic Bayes factors. The different default methods are first compared with each other and with the p-value in normal one-sides testing, to illustrate the basic issues. General results for one-sides testing in location and scale models are then presented. The default Bayes factors are also studied for specific models involving multiple hypotheses. In most of the examples presented we also derive the intrinsic prior; this is the prior distribution which, if used directly, would yield answers (asymtotically) equivalent to those for the given default Bayes factor.Bayes factor, fractional Bayes factor, intrinsic Bayes factor, model comparison, one-sided hypothesis testing, multiple hypothesistesting