#### 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)