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Benchmark priors for Bayesian Model averaging

Author

Listed:
  • Carmen Fernández
  • Eduardo Ley
  • Mark F. J. Steel

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. In addition, 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Carmen Fernández & Eduardo Ley & Mark F. J. Steel, "undated". "Benchmark priors for Bayesian Model averaging," Working Papers 98-06, FEDEA.
  • Handle: RePEc:fda:fdaddt:9806
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    References listed on IDEAS

    as
    1. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters, in: Essays in the Economics of Crime and Punishment, pages 1-54, National Bureau of Economic Research, Inc.
    2. Chib, B. & Osiewalski, J. & Steel, M., 1990. "Regression Models Under Competing Covariance Matrices: A Baysian Perspective," Papers 9063, Tilburg - Center for Economic Research.
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    4. Akaike, Hirotugu, 1981. "Likelihood of a model and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 3-14, May.
    5. 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.
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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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