ON PROPERTIES OF PREDICTIVE PRIORS IN LINEAR-MODELS

Utilizing the notion of matching predictives as in Berger and Pericchi , we show that for the conjugate family of prior distributions in the normal linear model, the symmetric Kullback-Leibler divergence between two particular predictive densities is minimized when the prior hyper parameters are taken to be those corresponding to the predictive prior s proposed in Ibrahim and Laud and Laud and Ibrahim. The main applicat ion for this result is for Bayesian variable selection.