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Benchmark priors for Bayesian model averaging

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  • Fernandez, Carmen
  • Ley, Eduardo
  • Steel, Mark F. J.

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 100 (2001)
Issue (Month): 2 (February)
Pages: 381-427

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Handle: RePEc:eee:econom:v:100:y:2001:i:2:p:381-427

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Luc BAUWENS, 1991. "The 'pathology' of the Natural Conjugate Prior Density in the Regression Model," Annales d'Economie et de Statistique, ENSAE, issue 23, pages 49-64.
  2. Gary S. Becker, 1968. "Crime and Punishment: An Economic Approach," Journal of Political Economy, University of Chicago Press, vol. 76, pages 169.
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  10. Ehrlich, Isaac, 1973. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 521-65, May-June.
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  12. Poirier, Dale J, 1988. "Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics," Journal of Economic Perspectives, American Economic Association, vol. 2(1), pages 121-44, Winter.
  13. Richard, J. F. & Steel, M. F. J., 1988. "Bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 7-37.
  14. Isaac Ehrlich, 1973. "The Deterrent Effect of Capital Punishment: A Question of Life and Death," NBER Working Papers 0018, National Bureau of Economic Research, Inc.
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  16. Jacek OSIEWALSKI & Mark F.J. STEEL, 1993. "Regression Models under Competing Covariance Structures: A Bayesian Perspective," Annales d'Economie et de Statistique, ENSAE, issue 32, pages 65-79.
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