# Calibration

Calibration is the property of forecasts, and can be united with resolution into calibration-cum-resolution. If the outcome is {$y_n$}, the the forecasts {$\gamma_n$} have this property, if

{$\frac{\sum_{n=1,\dots,N: \gamma_n \approx \gamma^*} (y_n-\gamma_n)\} } { \sum_{n=1,\dots,N: \gamma_n \approx \gamma^*} 1 \} }\approx 0$}.

The algorithm achieves the asymptotic calibration-cum-resolution, if

{$\lim\limits_{N \to \infty} \frac{1}{N} \sum_{n=1}^N (y_n - \gamma_n) f(\gamma_n) = 0$}

for all continuous functions {$f: [0,1] \times X \to \mathbb{R}$} from some class.

In case of weather forecasts, calibration means that forecaster is good in prediction of the probability of rain (it was raining in 70% of the days, when the forecaster predicted 70% probability of rain).

### Bibliography

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