TWO-SAMPLE BAYESIAN TESTS USING INTRINSIC BAYES FACTORS FOR MULTIVARIATE NORMAL OBSERVATIONS

Abstract

Unlike estimation problems, it is necessary to be careful to use noninformative priors in Bayesian model selection or testing problems. Since these priors are typically improper and are defined only up to arbitrary constants, the resulting Bayes factors are then not well defined. A recently proposed model selection criterion, the intrinsic Bayes factor (IBF), overcomes such problems by using a part of the sample as a training sample. In this article, the IBF criterion was used to conduct a multiple test of two independent multivariate normal populations, which is commonly used in longitudinal data analysis and repeated measurements experiments. Finally, a simulation study was performed to support theoretical results.