- Brier score
A Brier score is a proper score function that measures the accuracy of a set of
probability assessments. Proposed by Brier (1950), it is the average squared deviation between predicted probabilities for a set of events and their outcomes, so a lower score represents higher accuracy.Definition of the Brier Score
:Suppose it is required to give a probability P forecast of a binary event – such as a forecast of rain. The forecast issued says that there is a probability P that the event will occur. Let X = 1 if the event occurs and X = 0 if it doesn’t.
Then the Brier score is given by: .
* If you forecast 100% (P = 1) and there is at least 1 mm of rain in the bucket, your Brier Score is 0, or "perfect".
* If you forecast 100% P and there is no rain in the bucket, your Brier Score is 1, or "awful".
* If you forecast 70% P and there is at least 1 mm of rain in the bucket, your Brier Score is (0.70-1)^2 = 0.09, or "not too shabby".
* If you forecast 30% P and there is at least 1 mm of rain in the bucket, your Brier Score is (0.30-1)^2 = 0.49, or "needs work".
* If you hedge your forecast with a 50% Pi and whether or not there is at least 1 mm of rain in the bucket, your Brier Score is 0.25, or "no courage".In weather forecasting, a trace (<0.01) is considered "0.0"
References
* [http://armstrong.wharton.upenn.edu/dictionary/definitions/brier%20score.html J. Scott Armstrong, "Principles of Forecasting"] .
* [http://amsglossary.allenpress.com/glossary/browse?s=b&p=43 AMS Glossary of Meteorology]
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