TY - JOUR
T1 - Calibrated Forecasting and Merging
AU - Kalai, Ehud
AU - Lehrer, Ehud
AU - Smorodinsky, Rann
N1 - Funding Information:
Consider a ®nite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the correct (but unknown) probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with the forecasted probabilities. This paper links unobserved reliability of forecasts to their observed empirical performance by demonstrating full equivalence between notions of merging and of calibration, and discusses implications of this equivalence for the literature of forecasting and learning. Journal of Economic Literature Classi®cation Numbers: C5, C11, C73, D83. Q 1999 Academic Press *The authors thank Robert Aumann, Dean Foster, John Hillas, Dov Samet, and Alvaro Sandroni for helpful comments. The research of Kalai and Lehrer is partly supported by the National Science Foundation Economics Grant No. SBR-9223156 and SBR-9515421. ²e-mail: [email protected]. ³e-mail: [email protected]. §e-mail: [email protected].
PY - 1999/10
Y1 - 1999/10
N2 - Consider a finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the correct (but unknown) probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with the forecasted probabilities. This paper links unobserved reliability of forecasts to their observed empirical performance by demonstrating full equivalence between notions of merging and of calibration, and discusses implications of this equivalence for the literature of forecasting and learning. Journal of Economic Literature Classification Numbers: C5, C11, C73, D83.
AB - Consider a finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the correct (but unknown) probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with the forecasted probabilities. This paper links unobserved reliability of forecasts to their observed empirical performance by demonstrating full equivalence between notions of merging and of calibration, and discusses implications of this equivalence for the literature of forecasting and learning. Journal of Economic Literature Classification Numbers: C5, C11, C73, D83.
UR - http://www.scopus.com/inward/record.url?scp=0011530965&partnerID=8YFLogxK
U2 - 10.1006/game.1998.0608
DO - 10.1006/game.1998.0608
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AN - SCOPUS:0011530965
SN - 0899-8256
VL - 29
SP - 151
EP - 169
JO - Games and Economic Behavior
JF - Games and Economic Behavior
IS - 1
ER -