Bernoulli

  • Bernoulli
  • Volume 16, Number 1 (2010), 155-180.

On the posterior distribution of classes of random means

Lancelot F. James, Antonio Lijoi, and 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 now known 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’s) and mixtures of NRMI. In 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’s and also of the two-parameter Poisson–Dirichlet process.

Article information

Source
Bernoulli, Volume 16, Number 1 (2010), 155-180.

Dates
First available in Project Euclid: 12 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1265984707

Digital Object Identifier
doi:10.3150/09-BEJ200

Mathematical Reviews number (MathSciNet)
MR2648753

Zentralblatt MATH identifier
1200.62019

Keywords
Bayesian nonparametrics completely random measures means of random probability measures normalized random measures Poisson–Dirichlet process posterior distribution species sampling models

Citation

James, Lancelot F.; Lijoi, Antonio; Prünster, Igor. On the posterior distribution of classes of random means. Bernoulli 16 (2010), no. 1, 155--180. doi:10.3150/09-BEJ200. https://projecteuclid.org/euclid.bj/1265984707


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