Default Bayes factors for nonnested hypothesis testing

Bayesian hypothesis testing for nonnested hypotheses is studied, using vari ous "default" Bayes factors, such as the fractional Bayes factor, the media n 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 i ssues. General results for one-sided testing in location and scale models a re then presented. The default Bayes factors are also studied for specific models involving multiple hypotheses. In particular, a multiple hypothesis testing example involving a sequential clinical trial is discussed. In most of the examples presented we also derive the intrinsic prior; this is the prior distribution, which, if used directly, would yield answers (asymptoti cally) equivalent to those for the given default Bayes factor.