ABSTRACT
This chapter introduces multivariate Bayesian Regression model that requires some knowledge of Multivariate as well as Bayesian Statistics. It considers the unobservable sources to be observable or known. This is done so that the Bayesian Regression model may be introduced which will help lead to the Bayesian Source Separation models. A Regression model is used when it is believed that a set of dependent variables may be represented as being linearly related to a set of independent variables. The main results of performing a Bayesian Regression are estimates of the matrix of Regression coefficients and the error covariance matrix. Marginal posterior mean estimation of the parameters involves computing the marginal posterior distribution for each of the parameters and then computing mean estimates from these marginal posterior distributions. Conditional modal intervals may be computed by using the conditional distribution for a particular parameter given the modal values of the others.
