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On the posterior distribution of classes of random means

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Author Info

  • Lancelot F. James
  • Antonio Lijoi
  • Igor Prünster
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    Abstract

    The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are known by now for random Dirichlet means but little is known, especially in terms of posterior distributions, for classes of priors beyond the Dirichlet process. In this paper we consider normalized random measures with independent increments (NRMI) and mixtures of NRMI: for both cases we are able to provide exact expressions for the posterior distribution of their means. These general results are then specialized leading to distributional results for means of two important particular cases of NRMI and also of the two parameter Poisson-Dirichlet process.

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    File URL: http://www.carloalberto.org/assets/working-papers/no.134.pdf
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    Bibliographic Info

    Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 134.

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    Length: 24 pages
    Date of creation: 2009
    Date of revision:
    Handle: RePEc:cca:wpaper:134

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    Related research

    Keywords: Bayesian Nonparametrics; Completely random measures; Means of random probability measures; Normalized random measures; Poisson-Dirichlet process; Posterior distribution; Species sampling models;

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    Cited by:
    1. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.

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