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February 2010 On the posterior distribution of classes of random means
Lancelot F. James, Antonio Lijoi, Igor Prünster
Bernoulli 16(1): 155-180 (February 2010). DOI: 10.3150/09-BEJ200


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.


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Lancelot F. James. Antonio Lijoi. Igor Prünster. "On the posterior distribution of classes of random means." Bernoulli 16 (1) 155 - 180, February 2010.


Published: February 2010
First available in Project Euclid: 12 February 2010

zbMATH: 1200.62019
MathSciNet: MR2648753
Digital Object Identifier: 10.3150/09-BEJ200

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

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability


Vol.16 • No. 1 • February 2010
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