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Effective Scoring Rules for Probabilistic Forecasts

Author

Listed:
  • Daniel Friedman

    (University of California at Los Angeles)

Abstract
This paper studies the use of a scoring rule for the elicitation of forecasts in the form of probability distributions and for the subsequent evaluation of such forecasts. Given a metric (distance function) on a space of probability distributions, a scoring rule is said to be effective if the forecaster's expected score is a strictly decreasing function of the distance between the elicited and "true" distributions. Two simple, well-known rules (the spherical and the quadratic) are shown to be effective with respect to suitable metrics. Examples and a practical application (in Foreign Exchange rate forecasting) are also provided.

Suggested Citation

  • Daniel Friedman, 1983. "Effective Scoring Rules for Probabilistic Forecasts," Management Science, INFORMS, vol. 29(4), pages 447-454, April.
    • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:4:p:447-454
    DOI: 10.1287/mnsc.29.4.447
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    Citations

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    Cited by:

    1. Norde, Henk & Voorneveld, Mark, 2019. "Feasible best-response correspondences and quadratic scoring rules," SSE Working Paper Series in Economics 2019:2, Stockholm School of Economics.
    2. Leonard Smith & Emma Suckling & Erica Thompson & Trevor Maynard & Hailiang Du, 2015. "Towards improving the framework for probabilistic forecast evaluation," Climatic Change, Springer, vol. 132(1), pages 31-45, September.
    3. Radosveta Ivanova-Stenzel & Timothy C. Salmon, 2004. "Bidder Preferences among Auction Institutions," Economic Inquiry, Western Economic Association International, vol. 42(2), pages 223-236, April.
    4. Papakonstantinou, Athanasios & Bogetoft, Peter, 2017. "Multi-dimensional procurement auction under uncertain and asymmetric information," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1171-1180.
    5. J. Eric Bickel, 2007. "Some Comparisons among Quadratic, Spherical, and Logarithmic Scoring Rules," Decision Analysis, INFORMS, vol. 4(2), pages 49-65, June.
    6. Plott, Charles R. & Salmon, Timothy C., 2004. "The simultaneous, ascending auction: dynamics of price adjustment in experiments and in the UK3G spectrum auction," Journal of Economic Behavior & Organization, Elsevier, vol. 53(3), pages 353-383, March.
    7. Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
    8. D. Johnstone, 2007. "The Value of a Probability Forecast from Portfolio Theory," Theory and Decision, Springer, vol. 63(2), pages 153-203, September.
    9. Karl Schlag & James Tremewan & Joël Weele, 2015. "A penny for your thoughts: a survey of methods for eliciting beliefs," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 457-490, September.
    10. Wheatcroft Edward, 2021. "Evaluating probabilistic forecasts of football matches: the case against the ranked probability score," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(4), pages 273-287, December.
    11. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    12. Onkal, Dilek & Muradoglu, Gulnur, 1995. "Effects of feedback on probabilistic forecasts of stock prices," International Journal of Forecasting, Elsevier, vol. 11(2), pages 307-319, June.
    13. Arthur Carvalho & Stanko Dimitrov & Kate Larson, 2018. "On proper scoring rules and cumulative prospect theory," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 343-376, November.
    14. Karl Schlag & James Tremewan & Joël Weele, 2015. "A penny for your thoughts: a survey of methods for eliciting beliefs," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 457-490, September.
    15. Papakonstantinou, A. & Bogetoft, P., 2013. "Crowd-sourcing with uncertain quality - an auction approach," MPRA Paper 46055, University Library of Munich, Germany.
    16. 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.
    17. Atanasios Mitropoulos, 2001. "On the Measurement of the Predictive Success of Learning Theories in Repeated Games," Experimental 0110001, University Library of Munich, Germany.
    18. Wheatcroft, Edward, 2021. "Evaluating probabilistic forecasts of football matches: the case against the ranked probability score," LSE Research Online Documents on Economics 111494, London School of Economics and Political Science, LSE Library.
    19. Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.
    20. Nolan Miller & Paul Resnick & Richard Zeckhauser, 2005. "Eliciting Informative Feedback: The Peer-Prediction Method," Management Science, INFORMS, vol. 51(9), pages 1359-1373, September.
    21. Tang, Fang-Fang, 2003. "A comparative study on learning in a normal form game experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 50(3), pages 385-390, March.
    22. Alexandre Vasconcelos Lima & Rogério Boueri Miranda & Mathias Schneid Tessmann, 2022. "Evaluation of the Future Price of Brazilian Commodities as a Predictor of the Price of the Spot Market," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 14(4), pages 1-51, April.

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    Keywords

    forecasting; Delphi technique;

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