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Abstract : |
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? In other words, on the subset of days where we forecast 2/3 chance of a particular event occurring, about 2/3 of the time that event should occur. 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 isn't allowed to randomize, then Nature wins---there will always be data for which the forecaster does poorly. This paper shows that if the forecaster can randomize, the forecaster wins in the sense that the forecasted probabilities and the empirical probabilities can be made arbitrarily close to each other., |
