Irrational Exuberance: Correcting Bias in Probability Estimates

• 成果类型: Article
• 署名作者: James, Gareth M.; Radchenko, Peter; Rava, Bradley
• 署名单位: University of Southern California; University of Sydney
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1787175
• 发表日期: 2022
• 页码: 455-468
• 关键词: Empirical Bayes

摘要

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme probabilities can result in systematically underestimating the true level of uncertainty. We develop an empirical Bayes approach excess certainty adjusted probabilities (ECAP), using a variant of Tweedie's formula, which updates probability estimates to correct for selection bias. ECAP is a flexible nonparametric method, which directly estimates the score function associated with the probability estimates, so it does not need to make any restrictive assumptions about the prior on the true probabilities. ECAP also works well in settings where the probability estimates are biased. We demonstrate through theoretical results, simulations, and an analysis of two real world datasets, that ECAP can provide significant improvements over the original probability estimates.for this article are available online.