Optimal predictive model selection
Maria Maddalena Barbieri and James Berger
Often the goal of model selection is to choose a model for future
prediction, and it is natural to measure the accuracy of a future
prediction by squared error loss. Under the Bayesian approach, it
is commonly perceived that the optimal predictive model is the
model with highest posterior probability, but this is not
necessarily the case. In this paper we show that, for selection
among normal linear models, the optimal predictive model is often
the {\it median probability model}, which need not coincide with
the highest probability model.