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August 2010 Consistency of objective Bayes factors as the model dimension grows
Elías Moreno, F. Javier Girón, George Casella
Ann. Statist. 38(4): 1937-1952 (August 2010). DOI: 10.1214/09-AOS754


In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist. Assoc. 104 (2009) 1261–1271]. However, in models where the number of parameters increases as the sample size increases, properties of the Bayes factor are not totally understood. Here we study consistency of the Bayes factors for nested normal linear models when the number of regressors increases with the sample size. We pay attention to two successful tools for model selection [Schwarz Ann. Statist. 6 (1978) 461–464] approximation to the Bayes factor, and the Bayes factor for intrinsic priors [Berger and Pericchi J. Amer. Statist. Assoc. 91 (1996) 109–122, Moreno, Bertolino and Racugno J. Amer. Statist. Assoc. 93 (1998) 1451–1460].

We find that the the Schwarz approximation and the Bayes factor for intrinsic priors are consistent when the rate of growth of the dimension of the bigger model is O(nb) for b < 1. When b = 1 the Schwarz approximation is always inconsistent under the alternative while the Bayes factor for intrinsic priors is consistent except for a small set of alternative models which is characterized.


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Elías Moreno. F. Javier Girón. George Casella. "Consistency of objective Bayes factors as the model dimension grows." Ann. Statist. 38 (4) 1937 - 1952, August 2010.


Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1323.62024
MathSciNet: MR2676879
Digital Object Identifier: 10.1214/09-AOS754

Primary: 62F05
Secondary: 62J15

Keywords: Bayes factors , BIC , intrinsic priors , linear models , multiplicity of parameters , rate of growth

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • August 2010
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