Calibrated Forecasting and Merging

Posted: 7 Mar 2012

See all articles by Ehud Kalai

Ehud Kalai

Northwestern University - Kellogg School of Management

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Date Written: March 7, 2012

Abstract

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.

Keywords: merging, calibration, learning

JEL Classification: C5, C11, C73, D83

Suggested Citation

Kalai, Ehud and Lehrer, Ehud and Smorodinsky, Rann, Calibrated Forecasting and Merging (March 7, 2012). Games and Economic Behavior, Vol. 29, 1999. Available at SSRN: https://ssrn.com/abstract=2017424

Ehud Kalai

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Rann Smorodinsky (Contact Author)

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel

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