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Generalized Species Sampling Priors With Latent Beta Reinforcements

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  • Edoardo M. Airoldi
  • Thiago Costa
  • Federico Bassetti
  • Fabrizio Leisen
  • Michele Guindani

Abstract

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a novel and probabilistically coherent family of nonexchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes' modeling framework, and we describe a Markov chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet process mixtures and hidden Markov models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array comparative genomic hybridization (CGH) data. Supplementary materials for this article are available online.

Suggested Citation

  • Edoardo M. Airoldi & Thiago Costa & Federico Bassetti & Fabrizio Leisen & Michele Guindani, 2014. "Generalized Species Sampling Priors With Latent Beta Reinforcements," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1466-1480, December.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:508:p:1466-1480
    DOI: 10.1080/01621459.2014.950735
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    Cited by:

    1. Fortini, Sandra & Petrone, Sonia & Sporysheva, Polina, 2018. "On a notion of partially conditionally identically distributed sequences," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 819-846.
    2. Michele Guindani & Wesley O. Johnson, 2018. "More nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 239-251, June.
    3. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2021. "A Central Limit Theorem for Predictive Distributions," Mathematics, MDPI, vol. 9(24), pages 1-11, December.
    4. Sandra Fortini & Sonia Petrone, 2020. "Quasi‐Bayes properties of a procedure for sequential learning in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 1087-1114, September.
    5. Chen, Kunzhi & Shen, Weining & Zhu, Weixuan, 2023. "Covariate dependent Beta-GOS process," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    6. Berti, Patrizia & Dreassi, Emanuela & Pratelli, Luca & Rigo, Pietro, 2021. "Asymptotics of certain conditionally identically distributed sequences," Statistics & Probability Letters, Elsevier, vol. 168(C).

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