Neural Computation, Vol 7, 867-888, Copyright © 1995 by The MIT Press

REVIEWS

Methods for combining experts' probability assessments

RA Jacobs
Department of Brain and Cognitive Sciences, University of Rochester, NY 14627, USA.

This article reviews statistical techniques for combining multiple probability distributions. The framework is that of a decision maker who consults several experts regarding some events. The experts express their opinions in the form of probability distributions. The decision maker must aggregate the experts' distributions into a single distribution that can be used for decision making. Two classes of aggregation methods are reviewed. When using a supra Bayesian procedure, the decision maker treats the expert opinions as data that may be combined with its own prior distribution via Bayes' rule. When using a linear opinion pool, the decision maker forms a linear combination of the expert opinions. The major feature that makes the aggregation of expert opinions difficult is the high correlation or dependence that typically occurs among these opinions. A theme of this paper is the need for training procedures that result in experts with relatively independent opinions or for aggregation methods that implicitly or explicitly model the dependence among the experts. Analyses are presented that show that m dependent experts are worth the same as k independent experts where k < or = m. In some cases, an exact value for k can be given; in other cases, lower and upper bounds can be placed on k.

This article has been cited by other articles:

				Md. SHAHJAHAN and K. MURASE A Pruning Algorithm for Training Cooperative Neural Network Ensembles IEICE Trans D: Information, March 1, 2006; E89-D(3): 1257 - 1269. [Abstract] [PDF]

				D. M. Pennock and M. P. Wellman Graphical Models for Groups: Belief Aggregation and Risk Sharing Decision Analysis, September 1, 2005; 2(3): 148 - 164. [Abstract] [PDF]

				K. Hsiang Low, W. Kheng Leow, and M. H. Ang Jr. An Ensemble of Cooperative Extended Kohonen Maps for Complex Robot Motion Tasks Neural Comput., June 1, 2005; 17(6): 1411 - 1445. [Abstract] [Full Text] [PDF]