Calibrated Forecasting and Merging
Consider a general finite-state stochastic process governed by an unknown objective probability distribution. A forecaster, observing the system, assigns subjective probabilities to future states. The subjective forecast merges to the objective distribution if, with time, forecasted probabilities converge to the (unknown) correct probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with their forecasted probabilities. This paper links the unobserved reliability of forecasts to their observed empirical performance by showing full equilvalents between notions of merging and calibration.
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