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A Kullback-Leibler View of Linear and Log-Linear Pools

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  • Ali E. Abbas

    (Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

Abstract

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.

Suggested Citation

  • Ali E. Abbas, 2009. "A Kullback-Leibler View of Linear and Log-Linear Pools," Decision Analysis, INFORMS, vol. 6(1), pages 25-37, March.
    • Handle: RePEc:inm:ordeca:v:6:y:2009:i:1:p:25-37
    DOI: 10.1287/deca.1080.0133
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    References listed on IDEAS

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    Cited by:

    1. Jason R. W. Merrick & Fabrizio Ruggeri & Refik Soyer & L. Robin Keller, 2012. "From the Editors---Games and Decisions in Reliability and Risk," Decision Analysis, INFORMS, vol. 9(2), pages 81-85, June.
    2. L. Robin Keller, 2009. "From the Editor..," Decision Analysis, INFORMS, vol. 6(1), pages 1-3, March.
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    4. L. Robin Keller & Ali Abbas & Manel Baucells & Vicki M. Bier & David Budescu & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Ahti Salo & George Wu, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(4), pages 327-330, December.
      • L. Robin Keller & Manel Baucells & Kevin F. McCardle & Gregory S. Parnell & Ahti Salo, 2007. "From the Editors..," Decision Analysis, INFORMS, vol. 4(4), pages 173-175, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
    5. L. Robin Keller, 2011. "From the Editor ---Multiattribute and Intertemporal Preferences, Probability, and Stochastic Processes: Models and Assessment," Decision Analysis, INFORMS, vol. 8(3), pages 165-169, September.
    6. Robert F. Bordley & Elena Katok & L. Robin Keller, 2010. "Honoring Michael H. Rothkopf's Legacy of Rigor and Relevance in Auction Theory: From the Editors," Decision Analysis, INFORMS, vol. 7(1), pages 1-4, March.
    7. L. Robin Keller & Kelly M. Kophazi, 2011. "From the Editors---Deterrence, Multiattribute Utility, and Probability and Bayes' Updating," Decision Analysis, INFORMS, vol. 8(2), pages 83-87, June.
    8. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Philippe Delquié & Kenneth C. Lichtendahl & Jason R. W. Merrick & Ahti Salo & George Wu, 2011. "From the Editors ---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis," Decision Analysis, INFORMS, vol. 8(4), pages 251-255, December.
    9. L. Robin Keller & Kelly M. Kophazi, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(2), pages 151-154, June.

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