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Calibration, sharpness and the weighting of experts in a linear opinion pool

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  • Stephen Hora
  • Erim Kardeş

Abstract

Linear opinion pools are the most common form of aggregating the probabilistic judgments of multiple experts. Here, the performance of such an aggregation is examined in terms of the calibration and sharpness of the component judgments. The performance is measured through the average quadratic score of the aggregate. Trade-offs between calibration and sharpness are examined and an expression for the optimal weighting of two dependent experts in a linear combination is given. Circumstances where one expert would be disqualified are investigated. Optimal weights for the multiple, dependent experts are found through a concave quadratic program. Copyright Springer Science+Business Media New York 2015

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  • Stephen Hora & Erim Kardeş, 2015. "Calibration, sharpness and the weighting of experts in a linear opinion pool," Annals of Operations Research, Springer, vol. 229(1), pages 429-450, June.
    • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:429-450:10.1007/s10479-015-1846-0
    DOI: 10.1007/s10479-015-1846-0
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    References listed on IDEAS

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    1. Morris H. DeGroot & Julia Mortera, 1991. "Optimal Linear Opinion Pools," Management Science, INFORMS, vol. 37(5), pages 546-558, May.
    2. Stephen C. Hora & Benjamin R. Fransen & Natasha Hawkins & Irving Susel, 2013. "Median Aggregation of Distribution Functions," Decision Analysis, INFORMS, vol. 10(4), pages 279-291, December.
    3. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    4. Hora, Stephen C. & Hora, Judith A. & Dodd, Nancy G., 1992. "Assessment of probability distributions for continuous random variables: A comparison of the bisection and fixed value methods," Organizational Behavior and Human Decision Processes, Elsevier, vol. 51(1), pages 133-155, February.
    5. Roopesh Ranjan & Tilmann Gneiting, 2010. "Combining probability forecasts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 71-91, January.
    6. Clements, Michael P. & Harvey, David I., 2011. "Combining probability forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 208-223, April.
    7. Stephen C. Hora, 2004. "Probability Judgments for Continuous Quantities: Linear Combinations and Calibration," Management Science, INFORMS, vol. 50(5), pages 597-604, May.
    8. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    9. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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    Cited by:

    1. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.

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