Predictive Model Selection

SUMMARY We consider the problem of selecting one model from a large class of plausible models. A predictive Bayesian viewpoint is advocated to avoid the specification 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 specification that emphasizes the observables, we implement the proposed methodology for three common problems arising in normal linear models: variable subset selection, selection of a transformation of predictor variables and 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.