IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v109y2014i507p1040-1053.html
   My bibliography  Save this article

Inference From Intrinsic Bayes' Procedures Under Model Selection and Uncertainty

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2014.880348
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2014.880348?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Ni, Shawn & Sun, Dongchu, 2003. "Noninformative priors and frequentist risks of bayesian estimators of vector-autoregressive models," Journal of Econometrics, Elsevier, vol. 115(1), pages 159-197, July.
    3. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
    4. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    5. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    6. 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.
    7. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    8. Berger J.O. & De Oliveira V. & Sanso B., 2001. "Objective Bayesian Analysis of Spatially Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1361-1374, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, vol. 8(2), pages 1-15, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    2. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    4. Minerva Mukhopadhyay & Tapas Samanta, 2017. "A mixture of g-priors for variable selection when the number of regressors grows with the sample size," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 377-404, June.
    5. Qifan Song & Guang Cheng, 2020. "Bayesian Fusion Estimation via t Shrinkage," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 353-385, August.
    6. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    7. Gilles Celeux & Mohammed El Anbari & Jean-Michel Marin & Christian P. Robert, 2010. "Regularization in Regression : Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation," Working Papers 2010-43, Center for Research in Economics and Statistics.
    8. Xueying Tang & Xiaofan Xu & Malay Ghosh & Prasenjit Ghosh, 2018. "Bayesian Variable Selection and Estimation Based on Global-Local Shrinkage Priors," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 215-246, August.
    9. P. Richard Hahn & Carlos M. Carvalho, 2015. "Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 435-448, March.
    10. Arnab Kumar Maity & Sanjib Basu & Santu Ghosh, 2021. "Bayesian criterion‐based variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 835-857, August.
    11. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    12. Li, Hanning & Pati, Debdeep, 2017. "Variable selection using shrinkage priors," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 107-119.
    13. Martin Feldkircher & Florian Huber & Gary Koop & Michael Pfarrhofer, 2022. "APPROXIMATE BAYESIAN INFERENCE AND FORECASTING IN HUGE‐DIMENSIONAL MULTICOUNTRY VARs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1625-1658, November.
    14. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    15. Bernardi, Mauro & Costola, Michele, 2019. "High-dimensional sparse financial networks through a regularised regression model," SAFE Working Paper Series 244, Leibniz Institute for Financial Research SAFE.
    16. 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.
    17. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    18. Lee Anthony & Caron Francois & Doucet Arnaud & Holmes Chris, 2012. "Bayesian Sparsity-Path-Analysis of Genetic Association Signal using Generalized t Priors," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(2), pages 1-31, January.
    19. Michael Pfarrhofer, 2024. "Forecasts with Bayesian vector autoregressions under real time conditions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(3), pages 771-801, April.
    20. Valen E. Johnson & David Rossell, 2010. "On the use of non‐local prior densities in Bayesian hypothesis tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 143-170, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1040-1053. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.