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Projective Limit Random Probabilities on Polish Spaces

Orbanz, P (2011) Projective Limit Random Probabilities on Polish Spaces. Electronic Journal of Statistics, 5. pp. 4-1373.

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: math.ST math.ST stat.ML stat.TH
Subjects: UNSPECIFIED
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:31
Last Modified: 10 Mar 2014 17:24
DOI: 10.1214/11-EJS641

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