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.