Bayesian Inference for the Precision Matrix for Scale Mixtures of Normal Distributions

Abstract

Baysian inference is considered for the precision matrix of the multivariate regression model with distribution of the random responses belonging to the multivariate scale mixtures of normal distributions. The posterior distribution and some identities involving expectations taken with respect to this posterior distribution are derived when the prior distribution of the parameters is from the conjugate family. The results are specialized to the case where the random responses have a matrix-t distribution and thus generalizing the results of Zellner (1976) and Muirhead (1986).