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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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