Evaluating probability forecasts

Details Evaluating probability forecasts Evaluating probability forecasts

2012-02-23

arxiv.org/abs/1202.5140v1

Annals of Statistics 2011, Vol. 39, No. 5, 2356-2382

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS902 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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