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An Objective Bayesian Criterion to Determine Model Prior Probabilities

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  • Cristiano Villa
  • Stephen Walker

Abstract

type="main" xml:id="sjos12145-abs-0001"> We discuss the problem of selecting among alternative parametric models within the Bayesian framework. For model selection problems, which involve non-nested models, the common objective choice of a prior on the model space is the uniform distribution. The same applies to situations where the models are nested. It is our contention that assigning equal prior probability to each model is over simplistic. Consequently, we introduce a novel approach to objectively determine model prior probabilities, conditionally, on the choice of priors for the parameters of the models. The idea is based on the notion of the worth of having each model within the selection process. At the heart of the procedure is the measure of this worth using the Kullback–Leibler divergence between densities from different models.

Suggested Citation

  • Cristiano Villa & Stephen Walker, 2015. "An Objective Bayesian Criterion to Determine Model Prior Probabilities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 947-966, December.
  • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:947-966
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    File URL: http://hdl.handle.net/10.1111/sjos.12145
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    References listed on IDEAS

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    1. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    2. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    3. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
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    Cited by:

    1. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    2. Steel, Mark F. J., 2017. "Model Averaging and its Use in Economics," MPRA Paper 90110, University Library of Munich, Germany, revised 16 Nov 2018.
    3. Hinoveanu, Laurentiu C. & Leisen, Fabrizio & Villa, Cristiano, 2019. "Bayesian loss-based approach to change point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 61-78.
    4. Grazian, Clara & Villa, Cristiano & Liseo, Brunero, 2020. "On a loss-based prior for the number of components in mixture models," Statistics & Probability Letters, Elsevier, vol. 158(C).

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