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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
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    File URL: http://dx.doi.org/10.1287/mnsc.29.4.447
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. D. Johnstone, 2007. "The Value of a Probability Forecast from Portfolio Theory," Theory and Decision, Springer, vol. 63(2), pages 153-203, September.
    7. 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.
    8. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    9. 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.
    10. Atanasios Mitropoulos, 2001. "On the Measurement of the Predictive Success of Learning Theories in Repeated Games," Experimental 0110001, EconWPA.
    11. 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.
    12. Nolan Miller & Paul Resnick & Richard Zeckhauser, 2005. "Eliciting Informative Feedback: The Peer-Prediction Method," Management Science, INFORMS, vol. 51(9), pages 1359-1373, September.
    13. 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.

    More about this item

    Keywords

    forecasting; Delphi technique;

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