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Bayes model averaging with selection of regressors

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  • P. J. Brown
  • M. Vannucci
  • T. Fearn
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    Abstract

    When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution. Copyright 2002 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal Of The Royal Statistical Society Series B.

    Volume (Year): 64 (2002)
    Issue (Month): 3 ()
    Pages: 519-536

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    Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:519-536

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    Cited by:
    1. Ouysse, Rachida & Kohn, Robert, 2010. "Bayesian variable selection and model averaging in the arbitrage pricing theory model," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3249-3268, December.
    2. Theo S. Eicher & Chris Papageorgiou & Adrian E. Raftery, 2011. "Default priors and predictive performance in Bayesian model averaging, with application to growth determinants," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 30-55, January/F.
    3. Korobilis, Dimitris, 2008. "Forecasting in vector autoregressions with many predictors," MPRA Paper 21122, University Library of Munich, Germany.
    4. ter Braak, Cajo J.F., 2006. "Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1232-1242, November.
    5. Steven N. Durlauf & Andros Kourtellos & Chih Ming Tan, 2005. "How Robust Are the Linkages Between Religiosity and Economic Growth," Discussion Papers Series, Department of Economics, Tufts University 0510, Department of Economics, Tufts University.
    6. Nott, David J. & Leng, Chenlei, 2010. "Bayesian projection approaches to variable selection in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3227-3241, December.
    7. Simila, Timo & Tikka, Jarkko, 2007. "Input selection and shrinkage in multiresponse linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 406-422, September.
    8. Chen, Kun & Jiang, Wenxin & Tanner, Martin A., 2010. "A note on some algorithms for the Gibbs posterior," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1234-1241, August.

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