A Bayesian Approach to Selecting Covariates for Prediction

We consider the problem of selecting a regression model from a large class of possible models in the case where no true model is believed to exist. In practice few statisticians, or scientists who employ statistical methods, believe that a "true" model exists, but nonetheless they seek to select a model as a proxy from which they want to predict. Unlike much of the recent work in this area we address this problem explicitly. We develop Bayesian predictive model selection techniques when proper conjugate priors are used and obtain an easily computed expression for the model selection criterion. We also derive expressions for updating the value of the statistic when a predictor is dropped from the model and apply this approach to a large well-known data set.