PREDICTIVE VARIABLE SELECTION FOR THE MULTIVARIATE LINEAR-MODEL

We develop a predictive Bayesian approach to variable selection in the multivariate linear model. A criterion derived from the Bayesian pred ictive density is proposed and a calibration is provided for it. Refer ence and informative priors are discussed, and an automated method tha t focuses on the response variable is proposed for specifying informat ive priors for the regression parameters. Relationships between the pr oposed criterion and other several well-known criteria are examined. I llustrative examples involving real data are given to demonstrate the methodology.