Bayesian analysis in multivariate regression models with conjugate priors

Abstract

In this paper, we consider the full rank multivariate regression model with matrix elliptically contoured distributed errors. We formulate a conjugate prior distribution for matrix elliptical models and derive the posterior distributions of mean and scale matrices. In the sequel, some characteristics of regression matrix parameters are also proposed.

Keywords:

• conjugate prior
• generalized Wishart distribution
• matrix elliptical distribution
• inverse Laplace transform

AMS Classification:

• Primary: 62F15
• Secondary: 62H05

Acknowledgements

The authors would like to thank Prof. Ng (Murdoch University) for valuable and constructive comments and providing us with the reference by Ng,[9] associate editor and two reviewers for their helpful comments that led to adding many substantial details in the paper and pointing out the representation in Section 5. The first author's research is supported by Shahrood University, Iran.