PREDICTIVE MODEL SELECTION

We consider the problem of selecting one model from a large class of p lausible 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 cr iteria derived from a certain predictive density and a prior specifica tion that emphasizes the observables, we implement the proposed method ology for three common problems arising in normal linear models: varia ble subset selection, selection of a transformation of predictor varia bles 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.