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Choosing a Strictly Proper Scoring Rule

Author

Listed:
  • Edgar C. Merkle

    (Department of Psychological Sciences, University of Missouri, Columbia, Missouri 65211)

  • Mark Steyvers

    (Department of Cognitive Sciences, University of California, Irvine, Irvine, California 92697)

Abstract

Strictly proper scoring rules, including the Brier score and the logarithmic score, are standard metrics by which probability forecasters are assessed and compared. Researchers often find that one's choice of strictly proper scoring rule has minimal impact on one's conclusions, but this conclusion is typically drawn from a small set of popular rules. In the context of forecasting world events, we use a recently proposed family of proper scoring rules to study the properties of a wide variety of strictly proper rules. The results indicate that conclusions vary greatly across different scoring rules, so that one's choice of scoring rule should be informed by the forecasting domain. We then describe strategies for choosing a scoring rule that meets the needs of the forecast consumer, considering three unique families of proper scoring rules.

Suggested Citation

  • Edgar C. Merkle & Mark Steyvers, 2013. "Choosing a Strictly Proper Scoring Rule," Decision Analysis, INFORMS, vol. 10(4), pages 292-304, December.
    • Handle: RePEc:inm:ordeca:v:10:y:2013:i:4:p:292-304
    DOI: 10.1287/deca.2013.0280
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    References listed on IDEAS

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    1. D. J. Johnstone, 2011. "Economic Interpretation of Probabilities Estimated by Maximum Likelihood or Score," Management Science, INFORMS, vol. 57(2), pages 308-314, February.
    2. Victor Richmond R. Jose & Robert F. Nau & Robert L. Winkler, 2008. "Scoring Rules, Generalized Entropy, and Utility Maximization," Operations Research, INFORMS, vol. 56(5), pages 1146-1157, October.
    3. Hand D.J. & Vinciotti V., 2003. "Local Versus Global Models for Classification Problems: Fitting Models Where it Matters," The American Statistician, American Statistical Association, vol. 57, pages 124-131, May.
    4. David J. Johnstone, 2007. "The Parimutuel Kelly Probability Scoring Rule," Decision Analysis, INFORMS, vol. 4(2), pages 66-75, June.
    5. Victor Richmond R. Jose & Robert F. Nau & Robert L. Winkler, 2009. "Sensitivity to Distance and Baseline Distributions in Forecast Evaluation," Management Science, INFORMS, vol. 55(4), pages 582-590, April.
    6. R. Winkler & Javier Muñoz & José Cervera & José Bernardo & Gail Blattenberger & Joseph Kadane & Dennis Lindley & Allan Murphy & Robert Oliver & David Ríos-Insua, 1996. "Scoring rules and the evaluation of probabilities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(1), pages 1-60, June.
    7. 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.
    8. J. Eric Bickel, 2007. "Some Comparisons among Quadratic, Spherical, and Logarithmic Scoring Rules," Decision Analysis, INFORMS, vol. 4(2), pages 49-65, June.
    9. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    10. David J. Johnstone & Victor Richmond R. Jose & Robert L. Winkler, 2011. "Tailored Scoring Rules for Probabilities," Decision Analysis, INFORMS, vol. 8(4), pages 256-268, December.
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