Intrinsic Priors for Testing Ordered Exponential Means

In Bayesian model selection or testing problems, Bayes factors under proper priors have been very successful. In practice, however, limited information and time constraints often require us to use noninformative priors which are typically improper and are deened only up to arbitrary constants. The resulting Bayes factors are then not well deened. A recently proposed model selection criterion, the intrinsic Bayes factor, overcomes such problems by using a part of the sample as a training sample to get a proper posterior and then use the posterior as the prior for the remaining observations to compute the Bayes factor. Surprisingly, such a B a y es factor can also be computed directly from the full sample by using some proper priors, namely intrinsic priors. The present paper explains how to derive i n trinsic priors for ordered exponential means. Some simulation results are also given to illustrate the method and compare it with classical methods.