A reference Bayesian test for nested hypotheses and its relationship to the Schwartz criterion

Prior assumptions under the null and alternative hypotheses are required to compute a Bayes factor for testing a nested hypotheses in the presence of a nuisance parameter. It is shown that the Schwartz criterion can give a reasonably approximate solution to a Bayesian testing problem. In certain cases, the log of the Bayes factor can be approximated by the Schwartz criterion with an acceptable degree of error.