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Benchmark Priors for Bayesian Model Averaging

Carmen Fernandez, Eduardo Ley and Mark Steel ()
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Carmen Fernandez: University of Saint Andrews, UK

Econometrics from University Library of Munich, Germany

Abstract: In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, "diffuse'' priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an ``automatic'' or ``benchmark'' prior structure that can be used in such cases. We focus on the Normal linear regression model with uncertainty in the choice of regressors. We propose a partly noninformative prior structure related to a Natural Conjugate $g$-prior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter $g_{0j}$. The consequences of different choices for $g_{0j}$ are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of several choices of $g_{0j}$ in a simulation study. The use of the MC$^3$ algorithm of Madigan and York (1995), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a "benchmark'' prior specification in a linear regression context with model uncertainty.

Keywords: Bayes Factors; Markov chain Monte Carlo; Posterior odds; Prior elicitation (search for similar items in EconPapers)
JEL-codes: C11 C15 (search for similar items in EconPapers)
Pages: 30 pages
Date: 1998-04-02, Revised 2001-10-08
New Economics Papers: this item is included in nep-ecm and nep-gth
Note: Type of Document - PDF; pages: 30 ; figures: included. Published in the Journal of Econometrics,100:2 (February), pages 381-427, 2001.
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Journal Article: Benchmark priors for Bayesian model averaging (2001) Downloads
Working Paper: Benchmark priors for Bayesian model averaging (1998) Downloads
Working Paper: Benchmark priors for Bayesian model averaging (1998) Downloads
Working Paper: Benchmark priors for Bayesian Model averaging Downloads
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