A Consistency Theorem for Regular Conditional Distributions

Patrizia Berti; Pietro Rigo

Let (omega, beta) be a measurable space, An in B a sub-sigma-field and µn a random probability measure, n >= 1. In various frameworks, one looks for a probability P on B such that µn is a regular conditional distribution for P given An for all n. Conditions for such a P to exist are given. The conditions are quite simple when (omega, beta) is a compact Hausdorff space equipped with the Borel or the Bairesigma-field (as well as under other similar assumptions). Such conditions are then applied to Bayesian statistics.

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Year of publication:	2010
Authors:	Berti, Patrizia ; Rigo, Pietro
Publisher:	Pavia : University of Pavia, Department of Economics and Quantitative Methods
Subject:	Posterior distribution \| Random probability measure \| Regular conditional distribution \| Wahrscheinlichkeitsrechnung \| Probability theory \| Statistische Verteilung \| Statistical distribution \| Schätztheorie \| Estimation theory