EVALUATING PROBABILITY FORECASTS

• 成果类型: Article
• 署名作者: Lai, Tze Leung; Gross, Shulamith T.; Shen, David Bo
• 署名单位: Stanford University; City University of New York (CUNY) System; Baruch College (CUNY)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS902
• 发表日期: 2011
• 页码: 2356-2382
• 关键词: SCORING RULES; predictive accuracy; statistics; ability

摘要

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.