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June 2004 Optimal predictive model selection
Maria Maddalena Barbieri, James O. Berger
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Ann. Statist. 32(3): 870-897 (June 2004). DOI: 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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Maria Maddalena Barbieri. James O. Berger. "Optimal predictive model selection." Ann. Statist. 32 (3) 870 - 897, June 2004.


Published: June 2004
First available in Project Euclid: 24 May 2004

zbMATH: 1092.62033
MathSciNet: MR2065192
Digital Object Identifier: 10.1214/009053604000000238

Primary: 62F15
Secondary: 62C10

Keywords: Bayesian linear models , predictive distribution , squared error loss , Variable selection

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 3 • June 2004
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