UNSPECIFIED (1997) Conditionally externally Bayesian pooling operators in chain graphs. ANNALS OF STATISTICS, 25 (4). pp. 1740-1761. ISSN 0090-5364

Full text not available from this repository.

Abstract

We address the multivariate version of French's group decision problem where the m members of a group,who are jointly responsible for the decisions they should make, wish to combine their beliefs about the possible Values of n random variables into the group consensus probability distribution. We shall assume the group has agreed on the structure of associations of variables in a problem, as might be represented by a commonly agreed partially complete chain graph (PCG) we define in the paper. However, the members diverge about the actual conditional probability distributions for the variables in the common PCG. The combination algorithm we suggest they adopt is one which demands, at least on learning :information which is common to the members and which preserves the originally agreed BCG structure, that the pools of conditional distributions associated with the PCG are externally Bayesian (EB). We propose a characterization for such conditionally EB (CEB) poolings which is more general and flexible than the characterization proposed by Genest, McConway and Schervish. In particular, such a generalization allows the weights attributed to the joint probability assessments of different individuals in the pool to differ across the distinct components of each joint density. We show that the group's commitment to being CEB on chain elements:can be accomplished by the group being EB on the whole PCG when the group also agrees to perform the conditional poolings in an ordering compatible with evidence propagation in the graph.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ANNALS OF STATISTICS
Publisher:	INST MATHEMATICAL STATISTICS
ISSN:	0090-5364
Date:	August 1997
Volume:	25
Number:	4
Number of Pages:	22
Page Range:	pp. 1740-1761
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/14770

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item