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Can we forecast the probability of an arbitrary sequence of events happening so that the stated probability of an event happening is close to its empirical probability? We can view this prediction problem as a game played against Nature, where at the beginning of the game Nature picks a data sequence and the forecaster picks a forecasting algorithm. If the forecaster is not allowed to randomise, then Nature wins; there will always be data for which the forecaster does poorly. This paper shows that, if the forecaster can randomise, the forecaster wins in the sense that the forecasted probabilities and the empirical probabilities can be made arbitrarily close to each other.
This is a post-peer-review, pre-copyedit version of an article published in Biometrika.
Brier score, calibration, competitive ratio, regret, universal prediction of sequences, worst case
Foster, D. P., & Vohra, R. (1998). Asymptotic Calibration. Biometrika, 85 (2), 379-390. http://dx.doi.org/10.1093/biomet/85.2.379
Date Posted: 27 November 2017
This document has been peer reviewed.