Consecutive Bayes factor for the mean vector

Abstract

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 T² test and has various appealing properties in practical applications. It relies on data only through the T²-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.

Keywords:

• Minimal training sample
• partial Bayes factor
• intrinsic Bayes factor
• random Bayes factor
• fractional Bayes factor

Acknowledgments

We would like to thank the reviewer whose comments significantly improved the quality of this manuscript.