Calibration Assessment and Boldness-Recalibration for Binary Events

Probability predictions are essential to inform decision making in medicine, economics, image classification, sports analytics, entertainment, and many other fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, i.e., far from the base rate of the event. Predictions that satisfy these three criteria are informative for decision making. However, there is a fundamental tension between calibration and boldness, since calibration metrics can be high when predictions are overly cautious, i.e., non-bold. The purpose of this work is to develop a hypothesis test and Bayesian model selection approach to assess calibration, and a strategy for boldness-recalibration that enables practitioners to responsibly embolden predictions subject to their required level of calibration. Specifically, we allow the user to pre-specify their desired posterior probability of calibration, then maximally embolden predictions subject to this constraint. We verify the performance of our procedures via simulation, then demonstrate the breadth of applicability by applying these methods to real world case studies in each of the fields mentioned above. We find that very slight relaxation of calibration probability (e.g., from 0.99 to 0.95) can often substantially embolden predictions (e.g., widening Hockey predictions' range from .25-.75 to .10-.90)