# Calibration-cum-resolution

Calibration-cum-resolution is the property of forecasts that unites the calibration and resolution properties. Let the sequence of outcomes be (assumed binary), the sequence of forecasts be , and let be the signal used in forecasting . The forecasts have this property if

for all forecasts and all signals . A convenient (and easier to formalize) restatement of this property is: a prediction algorithm achieves asymptotic calibration-cum-resolution if

for all continuous functions from some class. Calibration corresponds to the case where does not depend on , and resolution to the case where does not depend on . In case of weather forecasts, calibration-cum-resolution means that forecaster is good in predicting of the probability of rain (it was raining in 70% of the days, when the forecaster predicted 70% probability of rain), and he is also good in predicting the weather "for Thursdays" (or for any other days, if we assess his forecasts only for these days).

### Bibliography

• Vladimir Vovk, Non-asymptotic calibration and resolution. Theoretical Computer Science (Special Issue devoted to ALT 2005) 387, 77–89 (2007).