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August 1997 Conditionally externally Bayesian pooling operators in chain graphs
Álvaro E. Faria Jr., Jim Q. Smith
Ann. Statist. 25(4): 1740-1761 (August 1997). DOI: 10.1214/aos/1031594740

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 PCG 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.

Citation

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Álvaro E. Faria Jr.. Jim Q. Smith. "Conditionally externally Bayesian pooling operators in chain graphs." Ann. Statist. 25 (4) 1740 - 1761, August 1997. https://doi.org/10.1214/aos/1031594740

Information

Published: August 1997
First available in Project Euclid: 9 September 2002

zbMATH: 0936.62006
MathSciNet: MR1463573
Digital Object Identifier: 10.1214/aos/1031594740

Subjects:
Primary: 62C10
Secondary: 62H99

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 4 • August 1997
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