Open Access
October 2011 Evaluating probability forecasts
Tze Leung Lai, Shulamith T. Gross, David Bo Shen
Ann. Statist. 39(5): 2356-2382 (October 2011). DOI: 10.1214/11-AOS902


Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient’s positive response to treatment. Scoring rules have long been used to assess the efficacy of the forecast probabilities after observing the occurrence, or nonoccurrence, of the predicted events. We develop herein a statistical theory for scoring rules and propose an alternative approach to the evaluation of probability forecasts. This approach uses loss functions relating the predicted to the actual probabilities of the events and applies martingale theory to exploit the temporal structure between the forecast and the subsequent occurrence or nonoccurrence of the event.


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Tze Leung Lai. Shulamith T. Gross. David Bo Shen. "Evaluating probability forecasts." Ann. Statist. 39 (5) 2356 - 2382, October 2011.


Published: October 2011
First available in Project Euclid: 30 November 2011

zbMATH: 1235.62127
MathSciNet: MR2906871
Digital Object Identifier: 10.1214/11-AOS902

Primary: 60G42 , 62P99
Secondary: 62P05

Keywords: forecasting , loss functions , Martingales , scoring rules

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 5 • October 2011
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