## The Annals of Statistics

### Optimal predictive model selection

#### Abstract

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

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

Dates
First available in Project Euclid: 24 May 2004

https://projecteuclid.org/euclid.aos/1085408489

Digital Object Identifier
doi:10.1214/009053604000000238

Mathematical Reviews number (MathSciNet)
MR2065192

Zentralblatt MATH identifier
1092.62033

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

#### Citation

Barbieri, Maria Maddalena; Berger, James O. Optimal predictive model selection. Ann. Statist. 32 (2004), no. 3, 870--897. doi:10.1214/009053604000000238. https://projecteuclid.org/euclid.aos/1085408489

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