PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Projective Limit Random Probabilities on Polish Spaces
Peter Orbanz
Electronic Journal of Statistics Volume 5, pp. 1354-1373, 2011.


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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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:8446
Deposited By:Peter Orbanz
Deposited On:08 January 2012