1. Why use several prediction metrics? | 2. Example data | 3. Start by looking at the predictions | 4. Calculate individual metrics | 4.1 RMSE: overall error magnitude | [\mathrm | 4.2 Bias: systematic overprediction or underprediction | [\mathrm | 5. A particularly important distinction: r2() versus R2() | 5.1 Lowercase r2() | [r^2 | 5.2 Uppercase R2() | [R^2 | 5.3 Correlation is not agreement | 6. Compare several models at once | 7. Categories of prediction performance metrics | 8. Core metrics | 9. Extended metrics | 9.1 Extended metric reference | 10. Quantile predictions | 11. How should metrics be combined? | 12. Related and redundant metrics | [\mathrm | 13. Missing values and special cases | 14. Practical recommendations | 15. References | 16. Next steps

1. Why validate predictive uncertainty? | 2. Which form of predictive uncertainty do you have? | 3. Functions used in this tutorial | 4. Example data | 5. Case A: predictive mean and standard deviation | 5.1 Prediction intervals | 5.1.1 Prediction interval coverage probability | 5.1.2 Coverage error | 5.1.3 Prediction interval width | 5.1.4 Interval score | 5.1.5 Calculate all interval diagnostics together | 5.2 Why calibration and sharpness must be considered together | 5.3 Reliability across multiple interval levels | 5.3.1 Numerical summaries of the reliability plot | 5.4 Why PICP alone is not enough | 5.5 Quantile coverage probability | 5.6 Probability integral transform | 5.7 Proper scoring rules | 5.7.1 Continuous ranked probability score | 5.7.2 Median CRPS | 5.7.3 Logarithmic score | 6. Case B: predictive distributions represented by samples | 6.1 Prediction intervals from predictive samples | 6.2 Reliability across interval levels from predictive samples | 6.3 Quantile calibration from predictive samples | 6.4 PIT from predictive samples | 6.5 CRPS from predictive samples | 6.6 CRPS reliability decomposition | 6.7 What about the logarithmic score with predictive samples? | 7. Comparing the two input formats | 8. A practical workflow | 8.1 If you only have prediction intervals | 8.2 If you have predicted quantiles | 8.3 If you have a predictive mean and standard deviation | 8.4 If you have predictive samples | 9. Recommended interpretation

1. Why use summary diagrams? | 2. Example data | 3. Solar diagram | [\mathrm | [\mathrm | [\mathrm | [\mathrm | [\mathrm | [\mathrm | 3.1 Reading a solar diagram | [\mathrm | 3.2 Basic solar diagram | 3.3 Colour models instead of writing labels | 3.4 Control the reference geometry | 4. Target diagram | 4.1 Reading a target diagram | 4.1.1 Note on the modelskill coordinate convention | 4.2 Basic target diagram | 4.3 Colour models with a legend | 4.4 Change the displayed range | 5. Taylor diagram | [\sigma^ | 5.1 The reference point | 5.2 Full Taylor diagram | 5.3 Half Taylor diagram | 5.4 Labels or legend | 5.5 Centred RMSD contours | 5.6 A limitation of the Taylor diagram | 6. Which diagram should I use? | 7. Customising the diagrams with ggplot2 | 7.1 Add titles and change the theme | 7.2 Move the legend | 7.3 Change the model colour palette | 7.4 Change the target axis titles | 7.5 Zoom without changing the statistics | 7.6 Change point and label sizes | 8. Practical recommendations

1. Why use several prediction metrics? | 2. Example data | 3. Start by looking at the predictions | 4. Calculate individual metrics | 4.1 RMSE: overall error magnitude | [\mathrm | 4.2 Bias: systematic overprediction or underprediction | [\mathrm | 5. A particularly important distinction: r2() versus R2() | 5.1 Lowercase r2() | [r^2 | 5.2 Uppercase R2() | [R^2 | 5.3 Correlation is not agreement | 6. Compare several models at once | 7. Categories of prediction performance metrics | 8. Core metrics | 9. Extended metrics | 9.1 Extended metric reference | 10. Quantile predictions | 11. How should metrics be combined? | 12. Related and redundant metrics | [\mathrm | 13. Missing values and special cases | 14. Practical recommendations | 15. References | 16. Next steps

1. Why validate predictive uncertainty? | 2. Which form of predictive uncertainty do you have? | 3. Functions used in this tutorial | 4. Example data | 5. Case A: predictive mean and standard deviation | 5.1 Prediction intervals | 5.1.1 Prediction interval coverage probability | 5.1.2 Coverage error | 5.1.3 Prediction interval width | 5.1.4 Interval score | 5.1.5 Calculate all interval diagnostics together | 5.2 Why calibration and sharpness must be considered together | 5.3 Reliability across multiple interval levels | 5.3.1 Numerical summaries of the reliability plot | 5.4 Why PICP alone is not enough | 5.5 Quantile coverage probability | 5.6 Probability integral transform | 5.7 Proper scoring rules | 5.7.1 Continuous ranked probability score | 5.7.2 Median CRPS | 5.7.3 Logarithmic score | 6. Case B: predictive distributions represented by samples | 6.1 Prediction intervals from predictive samples | 6.2 Reliability across interval levels from predictive samples | 6.3 Quantile calibration from predictive samples | 6.4 PIT from predictive samples | 6.5 CRPS from predictive samples | 6.6 CRPS reliability decomposition | 6.7 What about the logarithmic score with predictive samples? | 7. Comparing the two input formats | 8. A practical workflow | 8.1 If you only have prediction intervals | 8.2 If you have predicted quantiles | 8.3 If you have a predictive mean and standard deviation | 8.4 If you have predictive samples | 9. Recommended interpretation

1. Why use summary diagrams? | 2. Example data | 3. Solar diagram | [\mathrm | [\mathrm | [\mathrm | [\mathrm | [\mathrm | [\mathrm | 3.1 Reading a solar diagram | [\mathrm | 3.2 Basic solar diagram | 3.3 Colour models instead of writing labels | 3.4 Control the reference geometry | 4. Target diagram | 4.1 Reading a target diagram | 4.1.1 Note on the modelskill coordinate convention | 4.2 Basic target diagram | 4.3 Colour models with a legend | 4.4 Change the displayed range | 5. Taylor diagram | [\sigma^ | 5.1 The reference point | 5.2 Full Taylor diagram | 5.3 Half Taylor diagram | 5.4 Labels or legend | 5.5 Centred RMSD contours | 5.6 A limitation of the Taylor diagram | 6. Which diagram should I use? | 7. Customising the diagrams with ggplot2 | 7.1 Add titles and change the theme | 7.2 Move the legend | 7.3 Change the model colour palette | 7.4 Change the target axis titles | 7.5 Zoom without changing the statistics | 7.6 Change point and label sizes | 8. Practical recommendations