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On the posterior distribution of classes of random means


  • Lancelot F. James
  • Antonio Lijoi
  • Igor Prünster


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.

Suggested Citation

  • Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "On the posterior distribution of classes of random means," Carlo Alberto Notebooks 134, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:134

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    References listed on IDEAS

    1. Stefano Mazzuco & Letizia Mencarini & Rosella Rettaroli, 2006. "Similarities and differences between two cohorts of young adults in Italy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(5), pages 105-146, September.
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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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