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May 2015 Approximate Bayesian Model Selection with the Deviance Statistic
Leonhard Held, Daniel Sabanés Bové, Isaac Gravestock
Statist. Sci. 30(2): 242-257 (May 2015). DOI: 10.1214/14-STS510

Abstract

Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective parameter priors in the linear model. One important class are $g$-priors, which were recently extended from linear to generalized linear models (GLMs). We show that the resulting Bayes factors can be approximated by test-based Bayes factors (Johnson [ Scand. J. Stat. 35 (2008) 354–368]) using the deviance statistics of the models. To estimate the hyperparameter $g$, we propose empirical and fully Bayes approaches and link the former to minimum Bayes factors and shrinkage estimates from the literature. Furthermore, we describe how to approximate the corresponding posterior distribution of the regression coefficients based on the standard GLM output. We illustrate the approach with the development of a clinical prediction model for 30-day survival in the GUSTO-I trial using logistic regression.

Citation

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Leonhard Held. Daniel Sabanés Bové. Isaac Gravestock. "Approximate Bayesian Model Selection with the Deviance Statistic." Statist. Sci. 30 (2) 242 - 257, May 2015. https://doi.org/10.1214/14-STS510

Information

Published: May 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1332.62094
MathSciNet: MR3353106
Digital Object Identifier: 10.1214/14-STS510

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.30 • No. 2 • May 2015
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