IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v146y2019icp112-117.html
   My bibliography  Save this article

An elementary derivation of the Chinese restaurant process from Sethuraman’s stick-breaking process

Author

Listed:
  • Miller, Jeffrey W.

Abstract

The usual proof that Sethuraman’s stick-breaking process gives rise to the Chinese restaurant process is indirect, relying on abstract properties of the Dirichlet process. This note provides a direct elementary proof, without using any measure theory.

Suggested Citation

  • Miller, Jeffrey W., 2019. "An elementary derivation of the Chinese restaurant process from Sethuraman’s stick-breaking process," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 112-117.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:112-117
    DOI: 10.1016/j.spl.2018.11.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218303560
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.11.009?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. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
    3. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    4. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
    5. S. Favaro & A. Lijoi & I. Prünster, 2012. "On the stick-breaking representation of normalized inverse Gaussian priors," Biometrika, Biometrika Trust, vol. 99(3), pages 663-674.
    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. Lawless Caroline & Arbel Julyan, 2019. "A simple proof of Pitman–Yor’s Chinese restaurant process from its stick-breaking representation," Dependence Modeling, De Gruyter, vol. 7(1), pages 45-52, March.

    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. Huang, Yifan & Meng, Shengwang, 2020. "A Bayesian nonparametric model and its application in insurance loss prediction," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 84-94.
    2. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    3. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    4. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.
    5. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    6. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    7. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    8. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    9. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    10. Liverani, Silvia & Hastie, David I. & Azizi, Lamiae & Papathomas, Michail & Richardson, Sylvia, 2015. "PReMiuM: An R Package for Profile Regression Mixture Models Using Dirichlet Processes," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i07).
    11. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    12. Isadora Antoniano-Villalobos & Stephen G. Walker, 2016. "A Nonparametric Model for Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 126-142, January.
    13. Mahdi Hosseinpouri & Majid Jafari Khaledi, 2019. "An area-specific stick breaking process for spatial data," Statistical Papers, Springer, vol. 60(1), pages 199-221, February.
    14. Igari, Ryosuke & Hoshino, Takahiro, 2018. "A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 150-166.
    15. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    16. Chung, Hwan & Chang, Hsiu-Ching, 2012. "Bayesian approaches to the model selection problem in the analysis of latent stage-sequential process," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4097-4110.
    17. repec:jss:jstsof:40:i05 is not listed on IDEAS
    18. Monica Billio & Roberto Casarin & Luca Rossini, 2016. "Bayesian nonparametric sparse seemingly unrelated regression model (SUR)," Working Papers 2016:20, Department of Economics, University of Venice "Ca' Foscari".
    19. Tsuyoshi Kunihama & David B. Dunson, 2013. "Bayesian Modeling of Temporal Dependence in Large Sparse Contingency Tables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1324-1338, December.
    20. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    21. Luis E. Nieto-Barajas & Peter Müller & Yuan Ji & Yiling Lu & Gordon B. Mills, 2012. "A Time-Series DDP for Functional Proteomics Profiles," Biometrics, The International Biometric Society, vol. 68(3), pages 859-868, September.

    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:eee:stapro:v:146:y:2019:i:c:p:112-117. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.