Optimal predictive model selection

Details Optimal predictive model selection Optimal predictive model selection

2004-06-23

arxiv.org/abs/math/0406464v1

Annals of Statistics 2004, Vol. 32, No. 3, 870-897

Mathematics

Statistics Theory

Scientific paper

10.1214/009053604000000238

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 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.

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