The Annals of Statistics

Optimal predictive model selection

Maria Maddalena Barbieri and James O. Berger

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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.

Article information

Ann. Statist., Volume 32, Number 3 (2004), 870-897.

First available in Project Euclid: 24 May 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Bayesian linear models predictive distribution squared error loss variable selection


Barbieri, Maria Maddalena; Berger, James O. Optimal predictive model selection. Ann. Statist. 32 (2004), no. 3, 870--897. doi:10.1214/009053604000000238.

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