Consecutive Bayes factor for the mean vector

In this article, we propose an explicit closed-form fully objective Bayes factor for one-sample hypotheses testing of the mean vector of multivariate normal population. The proposed approach can be regarded as a Bayesian version of the Hotelling's T-2 test and has various appealing properties in practical applications. It relies on data only through the T-2-statistic and can easily be calculated. The proposed Bayes factor is applicable for the multivariate paired test as well as the univariate case. In this article, we also introduce a simple idea of consecutive minimal training samples which leads to a fully objective Bayes factor. Simulated and real data examples are provided for illustrative purposes.