PREDICTION-BASED MODEL SELECTION FOR BAYESIAN MULTIPLE REGRESSION MODELS

Model selection is an important part of model building for Bayesian linear models when the number of possible model terms is large. Most current approaches focus on posterior model probabilities or the deviance information criterion. This article proposes an alternative strategy that considers how the model will be used after its selection and selects models based on their predictive abilities over a user-specified portion of the covariate space defined by a joint probability distribution called the distribution of interest. Because it is difficult to summarize the "goodness" of a model with a single number, we present a suite of numerical and graphical tools for detailed comparisons of different models. These tools help in selecting a best model or a collection of good models based on their prediction performances over covariate locations likely to arise from the distribution of interest. The proposed method is illustrated with two examples. The first example motivates and illustrates the new method, while the second example considers what to do when comparing thousands of models. Simulation results demonstrate where the new method produces improvements in prediction ability over some existing methods.