Default Bayes Factors for Non-Nested Hypothesis Testing

James O. Berger and Julia Mortera

Bayesian hypothesis testing for non-nested hypotheses is studied, using 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-sided testing, to illustrate the basic issues. General results for one-sided 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 (asymptotically) equivalent to those for the given default Bayes factor. Postscript File (683kB)