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Inference From Intrinsic Bayes' Procedures Under Model Selection and Uncertainty

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  • Andrew J. Womack
  • Luis León-Novelo
  • George Casella

Abstract

In this article, we present a fully coherent and consistent objective Bayesian analysis of the linear regression model using intrinsic priors. The intrinsic prior is a scaled mixture of g -priors and promotes shrinkage toward the subspace defined by a base (or null) model. While it has been established that the intrinsic prior provides consistent model selectors across a range of models, the posterior distribution of the model parameters has not previously been investigated. We prove that the posterior distribution of the model parameters is consistent under both model selection and model averaging when the number of regressors is fixed. Further, we derive tractable expressions for the intrinsic posterior distribution as well as sampling algorithms for both a selected model and model averaging. We compare the intrinsic prior to other mixtures of g -priors and provide details on the consistency properties of modified versions of the Zellner-Siow prior and hyper g -priors. Supplementary materials for this article are available online.

Suggested Citation

  • Andrew J. Womack & Luis León-Novelo & George Casella, 2014. "Inference From Intrinsic Bayes' Procedures Under Model Selection and Uncertainty," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1040-1053, September.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1040-1053
    DOI: 10.1080/01621459.2014.880348
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    File URL: http://hdl.handle.net/10.1080/01621459.2014.880348
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
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    5. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
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    7. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    8. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
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    Cited by:

    1. J. A. Cano & M. Iniesta & D. Salmerón, 2018. "Integral priors for Bayesian model selection: how they operate from simple to complex cases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 968-987, December.
    2. T S Shively & S G Walker, 2018. "On Bayes factors for the linear model," Biometrika, Biometrika Trust, vol. 105(3), pages 739-744.
    3. Dimitris Fouskakis & Ioannis Ntzoufras, 2020. "Bayesian Model Averaging Using Power-Expected-Posterior Priors," Econometrics, MDPI, Open Access Journal, vol. 8(2), pages 1-15, May.

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