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A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability

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  • Petrone, Sonia
  • Raftery, Adrian E.

Abstract

We consider Bayesian nonparametric inference for continuous-valued partially exchangeable data, when the partition of the observations into groups is unknown. This includes change-point problems and mixture models. As the prior, we consider a mixture of products of Dirichlet processes. We show that the discreteness of the Dirichlet process can have a large effect on inference (posterior distributions and Bayes factors), leading to conclusions that can be different from those that result from a reasonable parametric model. When the observed data are all distinct, the effect of the prior on the posterior is to favor more evenly balanced partitions, and its effect on Bayes factors is to favor more groups. In a hierarchical model with a Dirichlet process as the second-stage prior, the prior can also have a large effect on inference, but in the opposite direction, towards more unbalanced partitions.

Suggested Citation

  • Petrone, Sonia & Raftery, Adrian E., 1997. "A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 69-83, November.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:1:p:69-83
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    Cited by:

    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. J. Griffin, 2011. "Bayesian clustering of distributions in stochastic frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(3), pages 275-283, December.
    3. Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2014. "Dependent mixture models: Clustering and borrowing information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 417-433.
    4. Guglielmi, Alessandra & Melilli, Eugenio, 2000. "Approximating de Finetti's measures for partially exchangeable sequences," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 309-315, July.
    5. Gebrenegus Ghilagaber & Parfait Munezero, 2020. "Bayesian change-point modelling of the effects of 3-points-for-a-win rule in football," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(2), pages 248-264, January.
    6. Hinoveanu, Laurentiu C. & Leisen, Fabrizio & Villa, Cristiano, 2019. "Bayesian loss-based approach to change point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 61-78.
    7. Huaiye Zhang & Inyoung Kim & Chun Gun Park, 2014. "Semiparametric Bayesian hierarchical models for heterogeneous population in nonlinear mixed effect model: application to gastric emptying studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2743-2760, December.
    8. Antonio Lijoi & Bernardo Nipoti & Igor Prünster, 2013. "Dependent mixture models: clustering and borrowing information," DEM Working Papers Series 046, University of Pavia, Department of Economics and Management.

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