# Resolution

Resolution is the property of forecasts, and can be united with calibration into calibration-cum-resolution. If the outcome is {`⚠ $y_n$`

}, the the forecasts {`⚠ $\gamma_n$`

} have this property, if

{`⚠ $\frac{\sum_{n=1,\dots,N: x_n \approx x^*} (y_n-\gamma_n)\} } { \sum_{n=1,\dots,N: x_n \approx x^*} 1\} }\approx 0$`

}.

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

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

}

for all continuous functions {`⚠ $f: [0,1] \times X \to \mathbb{R}$`

} from some class. In case of weather forecasts, resolution means that forecaster is good in prediction 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).