IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v28y2001i2p355-375.html
   My bibliography  Save this article

Modelling Heterogeneity With and Without the Dirichlet Process

Author

Listed:
  • Peter J. Green
  • Sylvia Richardson

Abstract

We investigate the relationships between Dirichlet process (DP) based models and allocation models for a variable number of components, based on exchangeable distributions. It is shown that the DP partition distribution is a limiting case of a Dirichlet–multinomial allocation model. Comparisons of posterior performance of DP and allocation models are made in the Bayesian paradigm and illustrated in the context of univariate mixture models. It is shown in particular that the unbalancedness of the allocation distribution, present in the prior DP model, persists a posteriori. Exploiting the model connections, a new MCMC sampler for general DP based models is introduced, which uses split/merge moves in a reversible jump framework. Performance of this new sampler relative to that of some traditional samplers for DP processes is then explored.

Suggested Citation

  • Peter J. Green & Sylvia Richardson, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 355-375, June.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:2:p:355-375
    DOI: 10.1111/1467-9469.00242
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9469.00242
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9469.00242?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
    ---><---

    Citations

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


    Cited by:

    1. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    2. Evelina Gabasova & John Reid & Lorenz Wernisch, 2017. "Clusternomics: Integrative context-dependent clustering for heterogeneous datasets," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-29, October.
    3. 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.
    4. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    5. Li, Mingyang & Meng, Hongdao & Zhang, Qingpeng, 2017. "A nonparametric Bayesian modeling approach for heterogeneous lifetime data with covariates," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 95-104.
    6. Ludkin, Matthew, 2020. "Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    7. Jing Wang, 2010. "Gibbs sampling in DP-based nonlinear mixed effects models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(2), pages 325-340.
    8. Congdon, P., 2007. "Bayesian modelling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2586-2601, February.
    9. Hedibert Freitas Lopes & Peter Müller & Gary L. Rosner, 2003. "Bayesian Meta-analysis for Longitudinal Data Models Using Multivariate Mixture Priors," Biometrics, The International Biometric Society, vol. 59(1), pages 66-75, March.
    10. Alessandra Guglielmi & Francesca Ieva & Anna M. Paganoni & Fabrizio Ruggeri & Jacopo Soriano, 2014. "Semiparametric Bayesian models for clustering and classification in the presence of unbalanced in-hospital survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 25-46, January.
    11. Lau, John W. & So, Mike K.P., 2008. "Bayesian mixture of autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 38-60, September.
    12. C. Yau & O. Papaspiliopoulos & G. O. Roberts & C. Holmes, 2011. "Bayesian non‐parametric hidden Markov models with applications in genomics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 37-57, January.
    13. Moya, Blake & Walker, Stephen G., 2024. "Full uncertainty analysis for Bayesian nonparametric mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    14. Alan P. Ker & Yong Liu, 2017. "Bayesian model averaging of possibly similar nonparametric densities," Computational Statistics, Springer, vol. 32(1), pages 349-365, March.
    15. Nathan Cunningham & Jim E. Griffin & David L. Wild, 2020. "ParticleMDI: particle Monte Carlo methods for the cluster analysis of multiple datasets with applications to cancer subtype identification," 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. 14(2), pages 463-484, June.
    16. J. Griffin, 2011. "Bayesian clustering of distributions in stochastic frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(3), pages 275-283, December.
    17. Rosella Castellano & Luisa Scaccia, 2007. "Bayesian inference for Hidden Markov Model," Working Papers 43-2007, Macerata University, Department of Finance and Economic Sciences, revised Oct 2008.
    18. Bettina Grün & Paul Hofmarcher, 2021. "Identifying groups of determinants in Bayesian model averaging using Dirichlet process clustering," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1018-1045, September.

    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:scjsta:v:28:y:2001:i:2:p:355-375. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.