Irrational Exuberance: Correcting Bias in Probability Estimates

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.

Automated summary

The paper presents an empirical Bayes approach called ECAP, which corrects for selection bias in probability estimates using a variant of Tweedie's formula. The method is flexible and does not rely on restrictive assumptions about prior probabilities. The authors demonstrate through theoretical analysis and real-world datasets that ECAP can significantly improve upon the original probability estimates.