Elements of information theory
Elements of information theory
Elicitation of Probabilities Using Competitive Scoring Rules
Decision Analysis
The Parimutuel Kelly Probability Scoring Rule
Decision Analysis
Decision Analysis
Decision Analysis
Decision Analysis
Decision Analysis
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
From the Editors---Games and Decisions in Reliability and Risk
Decision Analysis
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Linear and log-linear pools are widely used methods for aggregating expert belief. This paper frames the expert aggregation problem as a decision problem with scoring rules. We propose a scoring function that uses the Kullback-Leibler (KL) divergence measure between the aggregate distribution and each of the expert distributions. The asymmetric nature of the KL measure allows for a convenient scoring system for which the linear and log-linear pools provide the optimal assignment. We also propose a “goodness-of-fit” measure that determines how well each opinion pool characterizes its expert distributions, and also determines the performance of each pool under this scoring function. We work through several examples to illustrate the approach.