Mean length of prediction intervals (Sect. 4.2.4) plotted against RMSE (Sect. 4.2.2) before and after calibration using additive CQR and with and without filtering on high-density regions. Marker colors indicate empirical miscoverage rates (Sect. 4.2.3). The coverage guarantee (34) applies only after calibration (blue diamonds atop the solid lines). We notice that when filtering on high-density regions, the coverage property no longer holds (pink diamonds atop the dashed lines).