Predictive Model Selection

We consider the problem of selecting one model from a large class of plausible models. A predictive Bayesian viewpoint is advocated to avoid the speci cation of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model. Using criteria derived from a certain predictive density and a prior speci cation that emphasizes the observables, we implement the proposed methodology for three common problems arising in normal linear models : (i) variable subset selection (ii) selection of a transformation of predictor variables, and (iii) estimation of a parametric variance function. Interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria. Relationships between the proposed criteria and other well known criteria are examined.