A General Method of Incorporating Forecast Cost and Loss in Value Scores

William Briggs General Internal Medicine, Weill Cornell Medical College, New York, New York

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Abstract

In this note, the author shows how to incorporate cost for correct forecasts in the skill score statistical test developed by Briggs and Ruppert and how to extend this result to another value score developed by Wilks. It is then shown that both of these methods are special cases of a more general complete value score, where the loss and costs are allowed to be completely general.

Corresponding author address: William Briggs, General Internal Medicine, Weill Cornell Medical College, 525 E. 68th, Box 46, New York, NY 10021. Email: wib2004@med.cornell.edu

Abstract

In this note, the author shows how to incorporate cost for correct forecasts in the skill score statistical test developed by Briggs and Ruppert and how to extend this result to another value score developed by Wilks. It is then shown that both of these methods are special cases of a more general complete value score, where the loss and costs are allowed to be completely general.

Corresponding author address: William Briggs, General Internal Medicine, Weill Cornell Medical College, 525 E. 68th, Box 46, New York, NY 10021. Email: wib2004@med.cornell.edu

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  • Briggs, W. M., and D. Ruppert, 2004: Assessing the skill of yes/no forecasts for Markov observations. Preprints, 17th Conf. on Probability and Statistics in the Atmospheric Sciences, Seattle, WA, Amer. Meteor. Soc, CD-ROM, 2.2.

  • Briggs, W. M., and D. Ruppert, 2005: Assessing the skill of yes/no forecasts. Biometrics, 61 , 799807.

  • Briggs, W. M., M. Pocernich, and D. Ruppert, 2005: Incorporating misclassification error in skill assessment. Mon. Wea. Rev., 133 , 33823392.

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  • Hamill, T. M., 1999: Hypothesis tests for evaluating numerical precipitation forecasts. Wea. Forecasting, 14 , 155167.

  • Richardson, D. S., 2000: Skill and relative economic value of the ECMWF ensemble prediction system. Quart. J. Roy. Meteor. Soc., 126 , 649667.

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  • Self, S. G., 1987: Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Amer. Stat. Assoc., 82 , 605610.

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  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

  • Wilks, D. S., 2001: A skill score based on economic value for probability forecasts. Meteor. Appl., 8 , 209219.

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