I. Verdinelli et L. Wasserman, COMPUTING BAYES FACTORS USING A GENERALIZATION OF THE SAVAGE-DICKEY DENSITY RATIO, Journal of the American Statistical Association, 90(430), 1995, pp. 614-618
We present a simple method for computing Bayes factors. The method der
ives from observing that in general, a Bayes meter can be written as t
he product of a quantity called the Savage-Dickey density ratio and a
correction factor: both terms are easily estimated from posterior simu
lation. In some cases it is possible to do these computations without
ever evaluating the likelihood.