Open Access
2011 Projective limit random probabilities on Polish spaces
Peter Orbanz
Electron. J. Statist. 5: 1354-1373 (2011). DOI: 10.1214/11-EJS641


A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals—the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.


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Peter Orbanz. "Projective limit random probabilities on Polish spaces." Electron. J. Statist. 5 1354 - 1373, 2011.


Published: 2011
First available in Project Euclid: 19 October 2011

zbMATH: 1274.62076
MathSciNet: MR2842908
Digital Object Identifier: 10.1214/11-EJS641

Primary: 62C10
Secondary: 60G57

Keywords: Bayesian nonparametrics , Dirichlet processes , random probability measures

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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