IDEAS home Printed from https://ideas.repec.org/p/pav/wpaper/095.html
   My bibliography  Save this paper

Bayesian model comparison based on expected posterior priors for discrete decomposable graphical models

Author

Listed:
  • Guido Consonni

    (Department of Economics and Quantitative Methods, University of Pavia)

  • Monia Lupparelli

    (Department of Statistical Sciences, University of Bologna)

Abstract

The implementation of the Bayesian paradigm to model comparison can be problematic. In particular, prior distributions on the parameter space of each candidate model require special care. While it is well known that improper priors cannot be used routinely for Bayesian model comparison, we claim that in general the use of conventional priors (proper or improper) for model comparison should be regarded as suspicious, especially when comparing models having different dimensions. The basic idea is that priors should not be assigned separately under each model; rather they should be related across models, in order to acquire some degree of compatibility, and thus allow fairer and more robust comparisons. In this connection, the Expected Posterior Prior (EPP) methodology represents a useful tool. In this paper we develop a procedure based on EPP to perform Bayesian model comparison for discrete undirected decomposable graphical models, although our method could be adapted to deal also with Directed Acyclic Graph models. We present two possible approaches. One, based on imaginary data, requires to single-out a base-model, is conceptually appealing and is also attractive for the communication of results in terms of plausible ranges for posterior quantities of interest. The second approach makes use of training samples from the actual data for constructing the EPP. It is universally applicable, but has limited flexibility due to its inherent double-use of the data. The methodology is illustrated through the analysis of a 2 × 3 × 4 contingency table.

Suggested Citation

  • Guido Consonni & Monia Lupparelli, 2009. "Bayesian model comparison based on expected posterior priors for discrete decomposable graphical models," Quaderni di Dipartimento 095, University of Pavia, Department of Economics and Quantitative Methods.
  • Handle: RePEc:pav:wpaper:095
    as

    Download full text from publisher

    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q095.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Consonni, Guido & La Rocca, Luca, 2008. "Tests Based on Intrinsic Priors for the Equality of Two Correlated Proportions," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1260-1269.
    2. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
    Full references (including those not matched with items on IDEAS)

    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. Davide Altomare & Guido Consonni & Luca La Rocca, 2011. "Objective Bayesian Search of Gaussian DAG Models with Non-local Priors," Quaderni di Dipartimento 140, University of Pavia, Department of Economics and Quantitative Methods.
    2. Mark J. Meyer & Haobo Cheng & Katherine Hobbs Knutson, 2023. "Bayesian Analysis of Multivariate Matched Proportions with Sparse Response," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 490-509, July.
    3. Guido Consonni & Roberta Paroli, 2017. "Objective Bayesian Comparison of Constrained Analysis of Variance Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 589-609, September.
    4. Aitkin Murray, 2013. "Comments on the review of Statistical Inference," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 121-132, June.
    5. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607, July.
    6. Mulder, Joris, 2014. "Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 448-463.
    7. 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.
    8. J. Cano & D. Salmerón & C. Robert, 2008. "Integral equation solutions as prior distributions for Bayesian model selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 493-504, November.
    9. Roberta Paroli & Guido Consonni, 2020. "Objective Bayesian comparison of order-constrained models in contingency tables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 139-165, March.
    10. Ando, Tomohiro & Tsay, Ruey, 2010. "Predictive likelihood for Bayesian model selection and averaging," International Journal of Forecasting, Elsevier, vol. 26(4), pages 744-763, October.

    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:pav:wpaper:095. 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: Paolo Bonomolo (email available below). General contact details of provider: https://edirc.repec.org/data/dppavit.html .

    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.