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.

[1]  Ehud Lehrer,et al.  Compatible Measures and Merging , 1996, Math. Oper. Res..

[2]  Frank Hahn,et al.  On the Notion of Equilibrium in Economics: An Inaugural Lecture , 1973 .

[3]  S. Hart,et al.  A simple adaptive procedure leading to correlated equilibrium , 2000 .

[4]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[5]  D. Monderer,et al.  Belief Affirming in Learning Processes , 1997 .

[6]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[7]  D. Fudenberg,et al.  Conditional Universal Consistency , 1999 .

[8]  Ehud Lehrer,et al.  Merging Economic Forecasts , 1990 .

[9]  D. Fudenberg,et al.  Consistency and Cautious Fictitious Play , 1995 .

[10]  F. Hayek.  Economics and knowledge , 1937 .

[11]  Pierpaolo Battigalli,et al.  Learning and Convergence to Equilibrium in Repeated Strategic Interactions: An Introductory Survey , 1992 .

[12]  Ehud Kalai,et al.  Weak and Strong Merging of Opinions , 1994 .

[13]  David Oakes,et al.  Self-Calibrating Priors Do Not Exist , 1985 .

[14]  D. Blackwell,et al.  Merging of Opinions with Increasing Information , 1962 .

[15]  D. Fudenberg,et al.  An Easier Way to Calibrate , 1999 .

[16]  Yaw Nyarko.  Bayesian learning leads to correlated equilibria in normal form games , 1994 .

[17]  Dean P. Foster,et al.  Calibrated Learning and Correlated Equilibrium , 1997 .

[18]  Yaw Nyarko.  Bayesian Learning in Repeated Games Leads to Correlated Equilibria in Normal Form Games , 1992 .

[19]  Finn E. Kydland,et al.  Time to Build and Aggregate Fluctuations , 1982 .

[20]  A. Dawid.  The Well-Calibrated Bayesian , 1982 .

[21]  D. Fudenberg,et al.  Self-confirming equilibrium , 1993 .

[22]  Ehud Lehrer,et al.  Repeated Large Games with Incomplete Information , 1997 .

[23]  E. Kalai,et al.  Rational Learning Leads to Nash Equilibrium , 1993 .