Modified intrinsic Bayes factor for multivariate regression models

Abstract

The multivariate Regression model (MRM) is one of the most widely used models for multivariate statistical inference. In this paper, a closed-form and fully objective Bayes factor for comparing two MRMs is introduced. We also introduce a Bayes factor-based method for comparing several MRMs. It is well known that the arithmetic intrinsic Bayes factor (AIBF) does not satisfy the pairwise and multiple coherency conditions. So, the AIBF cannot be used in multiple hypotheses testing and model selection. Even in the case of only two competing hypothesis or models, lack of pairwise coherency leads to the embarrassing position of two Bayes factors for comparing two models instead of just one. In this paper, we have made a simple modification to the original definition and introduced the modified intrinsic Bayes factor (ModIBF) which satisfies the pairwise and the multiple coherency conditions.