Journal article
Sampling Uncertainty and Confidence Intervals for the Brier Score and Brier Skill Score
Weather and forecasting, Vol.23(5), pp.992-1006
10/01/2008
DOI: 10.1175/2007WAF2007049.1
Abstract
Abstract For probability forecasts, the Brier score and Brier skill score are commonly used verification measures of forecast accuracy and skill. Using sampling theory, analytical expressions are derived to estimate their sampling uncertainties. The Brier score is an unbiased estimator of the accuracy, and an exact expression defines its sampling variance. The Brier skill score (with climatology as a reference forecast) is a biased estimator, and approximations are needed to estimate its bias and sampling variance. The uncertainty estimators depend only on the moments of the forecasts and observations, so it is easy to routinely compute them at the same time as the Brier score and skill score. The resulting uncertainty estimates can be used to construct error bars or confidence intervals for the verification measures, or perform hypothesis testing. Monte Carlo experiments using synthetic forecasting examples illustrate the performance of the expressions. In general, the estimates provide very reliable information on uncertainty. However, the quality of an estimate depends on both the sample size and the occurrence frequency of the forecast event. The examples also illustrate that with infrequently occurring events, verification sample sizes of a few hundred forecast–observation pairs are needed to establish that a forecast is skillful because of the large uncertainties that exist.
Details
- Title: Subtitle
- Sampling Uncertainty and Confidence Intervals for the Brier Score and Brier Skill Score
- Creators
- A. Allen Bradley - IIHR-Hydroscience and Engineering, The University of Iowa, Iowa City, IowaStuart S Schwartz - Center for Urban Environmental Research and Education, University of Maryland, Baltimore County, Baltimore, MarylandTempei Hashino - Department of Atmospheric and Ocean Sciences, University of Wisconsin—Madison, Madison, Wisconsin
- Resource Type
- Journal article
- Publication Details
- Weather and forecasting, Vol.23(5), pp.992-1006
- DOI
- 10.1175/2007WAF2007049.1
- ISSN
- 0882-8156
- eISSN
- 1520-0434
- Language
- English
- Date published
- 10/01/2008
- Academic Unit
- Civil and Environmental Engineering
- Record Identifier
- 9983991990102771
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