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Optimal predictive model selection. (English) Zbl 1092.62033
Summary: 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. We show that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model. The median probability model often differs from the highest probability model.

MSC:
62F15Bayesian inference
62H12Multivariate estimation
62J05Linear regression
62C10Bayesian problems; characterization of Bayes procedures
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