Open Access
2009 Distributional properties of means of random probability measures
Antonio Lijoi, Igor Prünster
Statist. Surv. 3: 47-95 (2009). DOI: 10.1214/09-SS041


The present paper provides a review of the results concerning distributional properties of means of random probability measures. Our interest in this topic has originated from inferential problems in Bayesian Nonparametrics. Nonetheless, it is worth noting that these random quantities play an important role in seemingly unrelated areas of research. In fact, there is a wealth of contributions both in the statistics and in the probability literature that we try to summarize in a unified framework. Particular attention is devoted to means of the Dirichlet process given the relevance of the Dirichlet process in Bayesian Nonparametrics. We then present a number of recent contributions concerning means of more general random probability measures and highlight connections with the moment problem, combinatorics, special functions, excursions of stochastic processes and statistical physics.


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Antonio Lijoi. Igor Prünster. "Distributional properties of means of random probability measures." Statist. Surv. 3 47 - 95, 2009.


Published: 2009
First available in Project Euclid: 11 August 2009

zbMATH: 1190.62056
MathSciNet: MR2529667
Digital Object Identifier: 10.1214/09-SS041

Primary: 62E15 , 62F15
Secondary: 60G57

Keywords: Bayesian nonparametrics , Cifarelli–Regazzini identity , completely random measures , Dirichlet process , functionals of random probability measures , generalized Stieltjes transform , neutral to the right processes , normalized random measures , posterior distribution , random means , random probability measure , two–parameter Poisson–Dirichlet process

Rights: Copyright © 2009 The author, under a Creative Commons Attribution License

Vol.3 • 2009
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