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Abstract : The Bayes approach to Multivariate Analysis taken previously by Geisser and Cornfield (JRSS Series B, 1963 No. 2, pp. 368-376) is extended and given a more comprehensive treatment. Posterior joint and marginal densities are derived for vector means, linear combinations of means; simple and partial variances; simple, partial and multiple correlation coefficients. Also discussed are the posterior distributions of the canonical correlations and of the principal components. For the general multivariate linear hypothesis, it is demonstrated that the joint Bayesian posterior region for the elements of the regression matrix is equivalent to the usual confidence region for these parameters. The joint predictive density of a set of future observations generated by the linear hypothesis is obtained thus enabling one to specify the probability that a set of future observations will be contained in a particular region. (Author)
Seymour Geisser (Mon,) studied this question.