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Models beyond the Dirichlet process

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  • Antonio Lijoi
  • Igor Pruenster

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.

Suggested Citation

  • Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:23-2009
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2009/ICERwp23-09.pdf
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    References listed on IDEAS

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    1. Blum, J. & Susarla, V., 1977. "On the posterior distribution of a dirichlet process given randomly right censored observations," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 207-211, July.
    2. 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, March.
    3. 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.
    4. Stephen G. Walker & Paul Damien & PuruShottam W. Laud & Adrian F. M. Smith, 1999. "Bayesian Nonparametric Inference for Random Distributions and Related Functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 485-527.
    5. Ilenia Epifani, 2003. "Exponential functionals and means of neutral-to-the-right priors," Biometrika, Biometrika Trust, vol. 90(4), pages 791-808, December.
    6. Stephen G. Walker & Bani K. Mallick, 1997. "Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 845-860.
    7. 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.
    8. Antonio Lijoi & Igor Prünster, 2009. "Distributional properties of means of random probability measures," Carlo Alberto Notebooks 120, Collegio Carlo Alberto.
    9. 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.
    10. 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.
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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;The Classification Society, vol. 27(3), pages 389-403, November.

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