Intrinsic Priors for Testing Two Normal Means with Intrinsic Bayes Factors

ABSTRACT In this article we consider the problem of comparing two normal means with unknown common variance using a Bayesian approach. Conventional Bayes factors with improper non informative priors are not well defined. The intrinsic Bayes factors are used to overcome such a difficulty. We derive intrinsic priors whose Bayes factors are asymptotically equivalent to the corresponding intrinsic Bayes factors. We illustrate our results with numerical examples.