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Dependent mixture models: clustering and borrowing information

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  • Antonio Lijoi

    ()
    (Department of Economics and Management, University of Pavia and Collegio Carlo Alberto)

  • Bernardo Nipoti

    ()
    (University of Turin and Collegio Carlo Alberto)

  • Igor Prünster

    ()
    (University of Turin and Collegio Carlo Alberto)

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    Abstract

    Most of the Bayesian nonparametric models for non–exchangeable data that are used in applications are based on some extension to the multivariate setting of the Dirichlet process, the best known being MacEachern’s dependent Dirichlet process. A comparison of two recently introduced classes of vectors of dependent nonparametric priors, based on the Dirichlet and the normalized s–stable processes respectively, is provided. These priors are used to define dependent hierarchical mixture models whose distributional properties are investigated. Furthermore, their inferential performance is examined through an extensive simulation study. The models exhibit different features, especially in terms of the clustering behavior and the borrowing of information across studies. Compared to popular Dirichlet process based models, mixtures of dependent normalized s–stable processes turn out to be a valid choice being capable of more effectively detecting the clustering structure featured by the data.

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    File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0046.pdf
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    Bibliographic Info

    Paper provided by University of Pavia, Department of Economics and Management in its series DEM Working Papers Series with number 046.

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    Length: 37 pages
    Date of creation: Jun 2013
    Date of revision:
    Handle: RePEc:pav:demwpp:demwp0046

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    Keywords: Bayesian Nonparametrics; Dependent Process; Dirichlet process; Generalized P´olya urn scheme; Mixture models; Normalized s–stable process; Partially exchangeable random partition.;

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    2. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Bayesian Nonparametric Estimation of the Probability of Discovering New Species," Biometrika, Biometrika Trust, vol. 94(4), pages 769-786.
    3. 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.
    4. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Controlling the reinforcement in Bayesian non-parametric mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 715-740.
    5. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 36(1), pages 76-97.
    6. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(1), pages 105-120.
    7. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    8. Griffiths, R. C. & Milne, R. K., 1978. "A class of bivariate Poisson processes," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 380-395, September.
    9. Peter Müller & Fernando Quintana & Gary Rosner, 2004. "A method for combining inference across related nonparametric Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 735-749.
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