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Statistical Inference for Stochastic Processes

, Volume 8, Issue 3, pp 283–309 | Cite as

Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior

  • Antonio LijoiEmail author
  • Ramsés H. Mena
  • Igor Prünster
Article

Abstract

This paper considers a generalization of the Dirichlet process which is obtained by suitably normalizing superposed independent gamma processes having increasing integer-valued scale parameter. A comprehensive treatment of this random probability measure is provided. We prove results concerning its finite-dimensional distributions, moments, predictive distributions and the distribution of its mean. Most expressions are given in terms of multiple hypergeometric functions, thus highlighting the interplay between Bayesian Nonparametrics and special functions. Finally, a suitable simulation algorithm is applied in order to compute quantities of statistical interest.

Keywords

Bayesian nonparametric inference Dirichlet process generalized gamma convolutions Lauricella hypergeometric functions means of random probability measures predictive distributions 

AMS 200 Mathematics Subject Classifications

62F15 60G57 

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Copyright information

© Springer 2005

Authors and Affiliations

  • Antonio Lijoi
    • 1
    Email author
  • Ramsés H. Mena
    • 2
  • Igor Prünster
    • 3
    • 4
  1. 1.Dipartimento di Economia Politica e Metodi QuantitativiUniversità degli Studi di PaviaPaviaItaly
  2. 2.Departimento de Probabilidad y EstadisticaIIMAS-UNAM-MéxicoMexicoMexico
  3. 3.Dipartimento di Economia Politica e Metodi QuantitativiUniversità degli Studi di PaviaPaviaItaly
  4. 4.ICERTorinoItaly

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