Petra Friederichs - Chair of Statistics STAT
Petra Friederichs - Chair of Statistics STAT
Petra Friederichs - Chair of Statistics STAT
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Mesoscale Weather Prediction<br />
Statistical Postprocessing<br />
Applications<br />
Conclusions and Challenges<br />
Semi-Parametric Approaches<br />
Parametric Approaches<br />
Forecast Verification: Proper Scoring Rules<br />
Semi-parametric approach<br />
probability<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
F(1)<br />
F(10)<br />
density<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
quantile [mm/12h]<br />
50<br />
10<br />
3<br />
1<br />
0.3<br />
0.5 quantile<br />
0.75 quantile<br />
0.95 quantile<br />
0.0<br />
0.0<br />
0.1<br />
0.1 0.3 1 3 10 50<br />
rain [mm/12h]<br />
0.1 0.3 1 3 10 50<br />
rain [mm/12h]<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
probability<br />
◮ Logistic regression: π = 1 − F Y (y | X) = logit −1 (β T X)<br />
◮ Censored quantile regression: q = F −1<br />
Y (τ | X) = max(0, βT X)<br />
P.<strong>Friederichs</strong> Extreme weather 14 / 45
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