Asymptotic Calibration

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 sequenc... Ausführliche Beschreibung

1. Person: Foster, Dean P.
Weitere Personen: Vohra, Rakesh V. verfasserin
Quelle: in Biometrika : a journal for the statistical study of biological problems Vol. 85, No. 2 (1998), p. 379-390
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Format: Online-Artikel
Sprache: English
Veröffentlicht: 1998
Beschreibung: Online-Ressource
Schlagworte: research-article
Brier score
Calibration
Competitive ratio
Regret
Universal prediction of sequences
Worst case
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Anmerkung: Copyright: Copyright 1998 Biometrika Trust
Zusammenfassung: 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.
ISSN: 0006-3444

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