MODEL CHOICE IN GENERALIZED LINEAR-MODELS - A BAYESIAN-APPROACH VIA KULLBACK-LEIBLER PROJECTIONS

We propose a general Bayesian method of comparing models. The approach is based on the Kullback-Leibler distance between two families of mod els, one nested within the other. For each parameter value of a full m odel, we compute the projection of the model to the restricted paramet er space and the corresponding minimum distance. From the posterior di stribution of the minimum distance, we can judge whether or not a more parsimonious model is appropriate. We show how the projection method can be implemented for generalised linear model selection and we propo se some Markov chain Monte Carlo algorithms for its practical implemen tation in less tractable cases. We illustrate the method with examples .