IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v72y2010i2p253-268.html
   My bibliography  Save this article

Minimally informative prior distributions for non‐parametric Bayesian analysis

Author

Listed:
  • Christopher A. Bush
  • Juhee Lee
  • Steven N. MacEachern

Abstract

Summary. We address the problem of how to conduct a minimally informative, non‐parametric Bayesian analysis. The central question is how to devise a model so that the posterior distribution satisfies a few basic properties. The concept of ‘local mass’ provides the key to the development of the limiting Dirichlet process model. This model is then used to provide an engine for inference in the compound decision problem and for multiple‐comparisons inference in a one‐way analysis‐of‐variance setting. Our analysis in this setting may be viewed as a limit of the analyses that were developed by Escobar and by Gopalan and Berry. Computations for the analysis are described, and the predictive performance of the model is compared with that of mixture of Dirichlet processes models.

Suggested Citation

  • Christopher A. Bush & Juhee Lee & Steven N. MacEachern, 2010. "Minimally informative prior distributions for non‐parametric Bayesian analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 253-268, March.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:2:p:253-268
    DOI: 10.1111/j.1467-9868.2009.00735.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2009.00735.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2009.00735.x?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
    ---><---

    References listed on IDEAS

    as
    1. Stephen G. Walker & Paul Damien & PuruShottam W. Laud & Adrian F. M. Smith, 1999. "Bayesian Nonparametric Inference for Random Distributions and Related Functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 485-527.
    2. Fernando A. Quintana & Pilar L. Iglesias, 2003. "Bayesian clustering and product partition models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 557-574, May.
    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. Wang, Xue & Walker, Stephen G., 2017. "An optimal data ordering scheme for Dirichlet process mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 42-52.
    2. Abhijoy Saha & Sebastian Kurtek, 2019. "Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 104-143, February.

    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. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    2. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    3. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    4. Wang, Ketong & Porter, Michael D., 2018. "Optimal Bayesian clustering using non-negative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 395-411.
    5. Im, Yunju & Tan, Aixin, 2021. "Bayesian subgroup analysis in regression using mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    6. Xiang Zhang & Yanbing Zheng, 2014. "Nonparametric Bayesian inference for multivariate density functions using Feller priors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 321-340, June.
    7. L. G. Leon-Novelo & B. Nebiyou Bekele & P. Müller & F. Quintana & K. Wathen, 2012. "Borrowing Strength with Nonexchangeable Priors over Subpopulations," Biometrics, The International Biometric Society, vol. 68(2), pages 550-558, June.
    8. George Karabatsos & Stephen Walker, 2009. "A Bayesian Nonparametric Approach to Test Equating," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 211-232, June.
    9. J. Griffin, 2011. "Bayesian clustering of distributions in stochastic frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(3), pages 275-283, December.
    10. John J. McCall, 2004. "Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov," Metroeconomica, Wiley Blackwell, vol. 55(2‐3), pages 195-218, May.
    11. Fellingham, Gilbert W. & Kottas, Athanasios & Hartman, Brian M., 2015. "Bayesian nonparametric predictive modeling of group health claims," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 1-10.
    12. Griffin, J. E. & Steel, M. F. J., 2004. "Semiparametric Bayesian inference for stochastic frontier models," Journal of Econometrics, Elsevier, vol. 123(1), pages 121-152, November.
    13. Jim Q. Smith & Paul E. Anderson & Silvia Liverani, 2008. "Separation measures and the geometry of Bayes factor selection for classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 957-980, November.
    14. David B. Dunson & M. Watson & Jack A. Taylor, 2003. "Bayesian Latent Variable Models for Median Regression on Multiple Outcomes," Biometrics, The International Biometric Society, vol. 59(2), pages 296-304, June.
    15. Maura Mezzetti & Daniele Borzelli & Andrea d’Avella, 2022. "A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1245-1271, December.
    16. An Cheng & Tonghui Chen & Guogang Jiang & Xinru Han, 2021. "Can Major Public Health Emergencies Affect Changes in International Oil Prices?," IJERPH, MDPI, vol. 18(24), pages 1-13, December.
    17. Sylvia Frühwirth-Schnatter & Gertraud Malsiner-Walli, 2019. "From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 33-64, March.
    18. Krnjajic, Milovan & Kottas, Athanasios & Draper, David, 2008. "Parametric and nonparametric Bayesian model specification: A case study involving models for count data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2110-2128, January.
    19. Chai Jian & Wang Shubin & Xiao Hao, 2013. "Abrupt Changes of Global Oil Price," Journal of Systems Science and Information, De Gruyter, vol. 1(1), pages 38-59, February.
    20. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.

    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:bla:jorssb:v:72:y:2010:i:2:p:253-268. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.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.