On Bayesian Hotelling’s T 2 test for the mean

Abstract

The multivariate one-sample problem considers an independent random sample from a multivariate normal distribution with mean and unknown variance For a given real vector the interest is to assess the hypothesis This paper proposes a new Bayesian approach to this problem based on comparing the change in the Kullback-Leibler divergence from a priori to a posteriori via the relative belief ratio. Eliciting the prior is also considered. The use of the approach is illustrated through several examples.