On the Bayesian Estimation of Multivariate Regression

Abstract

Summary In this paper, we use a Bayesian approach to analyse sets of regression equations with correlated error terms. In the case that the matrix of “independent variables” is the same for all equations, our model reduces to the traditional multivariate regression model. For this case, the marginal posterior distribution of the regression coefficient vector for any equation is shown to be of the multivariate-t form. Further, the variances and covariances of the error terms have an “inverted” Wishart distribution a posteriori. Some properties of this distribution are given. Finally, the joint posterior distribution of the regression coefficients in the general model is derived and discussed.