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Models beyond the Dirichlet process

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  • Antonio Lijoi

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  • Igor Pruenster

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    Abstract

    Bayesian nonparametric inference is a relatively young area of research and it has recently undergone a strong development. Most of its success can be explained by the considerable degree of exibility it ensures in statistical modelling, if compared to parametric alternatives, and by the emergence of new and ecient simulation techniques that make nonparametric models amenable to concrete use in a number of applied statistical problems. Since its introduction in 1973 by T.S. Ferguson, the Dirichlet process has emerged as a cornerstone in Bayesian nonparametrics. Nonetheless, in some cases of interest for statistical applications the Dirichlet process is not an adequate prior choice and alternative nonparametric models need to be devised. In this paper we provide a review of Bayesian nonparametric models that go beyond the Dirichlet process.

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    File URL: http://www.icer.it/docs/wp2009/ICERwp23-09.pdf
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    Bibliographic Info

    Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 23-2009.

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    Length: 47 pages
    Date of creation: Dec 2009
    Date of revision:
    Handle: RePEc:icr:wpmath:23-2009

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    1. James, Lancelot F., 2003. "A simple proof of the almost sure discreteness of a class of random measures," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 363-368, December.
    2. Hanson T. & Johnson W.O., 2002. "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1020-1033, December.
    3. 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.
    4. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
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    Cited by:
    1. Ruth Fuentes–García & Ramsés Mena & Stephen Walker, 2010. "A Probability for Classification Based on the Dirichlet Process Mixture Model," Journal of Classification, Springer, vol. 27(3), pages 389-403, November.

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