Benchmark priors for Bayesian Model averaging
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.)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Gary S. Becker, 1968. "Crime and Punishment: An Economic Approach," Journal of Political Economy, University of Chicago Press, vol. 76, pages 169-169.
- Chib, S. & Osiewalski, J. & Steel, M.F.J., 1990. "Regression models under competing covariance matrices : A Bayesian perspective," Discussion Paper 1990-63, Tilburg University, Center for Economic Research.
- Chib, B. & Osiewalski, J. & Steel, M., 1990. "Regression Models Under Competing Covariance Matrices: A Baysian Perspective," Papers 9063, Tilburg - Center for Economic Research.
- Akaike, Hirotugu, 1981. "Likelihood of a model and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 3-14, May.
- 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.
- Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
- Smith, M. & Kohn, R., "undated". "Nonparametric Regression using Bayesian Variable Selection," Statistics Working Paper _009, Australian Graduate School of Management.
- Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, vol. 69(1), pages 289-331, September.
- Peter C.B. Phillips, 1992. "Bayesian Model Selection and Prediction with Empirical Applications," Cowles Foundation Discussion Papers 1023, Cowles Foundation for Research in Economics, Yale University.
- Hoeting, Jennifer & Raftery, Adrian E. & Madigan, David, 1996. "A method for simultaneous variable selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 251-270, July.
- Ehrlich, Isaac, 1975. "The Deterrent Effect of Capital Punishment: A Question of Life and Death," American Economic Review, American Economic Association, vol. 65(3), pages 397-417, June.
- 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.
- Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
- Min, C.K. & Zellner, A., 1992. ""Bayesian and Non-Bayesian Methods for Combining Models and Forecasts with Applications to Forecasting International Growth Rates"," Papers 90-92-23, California Irvine - School of Social Sciences.
- 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 121-144, Winter.
- Luc Bauwens, 1991. "The 'pathologie' of the Natural Conjugate Prior Density in the Regression Model," Annals of Economics and Statistics, GENES, issue 23, pages 49-64.
- Bauwens, L., 1990. "The "Pathology" Of The Natural Conjugate Prior Density In The Regression Model," G.R.E.Q.A.M. 90a14, Universite Aix-Marseille III.
- Cornwell, Christopher & Trumbull, William N, 1994. "Estimating the Economic Model of Crime with Panel Data," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 360-366, May.
- repec:adr:anecst:y:1993:i:32:p:04 is not listed on IDEAS
- Atkinson, A. C., 1981. "Likelihood ratios, posterior odds and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 15-20, May.
- Ehrlich, Isaac, 1973. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 521-565, May-June.
- Chow, Gregory C., 1981. "A comparison of the information and posterior probability criteria for model selection," Journal of Econometrics, Elsevier, vol. 16(1), pages 21-33, May. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:fda:fdaddt:9806. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carmen Arias)
If references are entirely missing, you can add them using this form.