Table D.1.
UQ metrics: Miscoverage rate and mean length of prediction intervals.
| Miscoverage rate (%) | Mean length of pred. intervals (×10−2) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Type of calibration | KS1 | KS2 | Wiener | MCALens | KS1 | KS2 | Wiener | MCALens | ||
| Uncalibrated | 6.94 ± 0.39 | 16.36 ± 1.09 | 36.04 ± 1.93 | 35.53 ± 1.89 | 11.43 ± 0.00 | 5.28 ± 0.00 | 2.65 ± 0.02 | 2.68 ± 0.02 | ||
| Add. | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.52 ± 0.61 | 4.52 ± 0.55 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.15 ± 0.02 | 7.13 ± 0.02 | ||
| Mult. | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.53 ± 0.60 | 4.51 ± 0.53 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.39 ± 0.04 | 7.35 ± 0.06 | ||
| χ2, a = 0.004 | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.53 ± 0.60 | 4.51 ± 0.54 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.31 ± 0.04 | 7.26 ± 0.05 | ||
| CQR | χ2, a = 0.006 | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.53 ± 0.60 | 4.51 ± 0.53 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.38 ± 0.04 | 7.33 ± 0.06 | |
| χ2, a = 0.008 | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.53 ± 0.60 | 4.51 ± 0.53 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.42 ± 0.05 | 7.37 ± 0.06 | ||
| χ2, a = 0.010 | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.53 ± 0.60 | 4.51 ± 0.53 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.45 ± 0.05 | 7.40 ± 0.07 | ||
| χ2, a = 0.012 | 4.49 ± 0.31 | 4.53 ± 0.53 | 4.53 ± 0.60 | 4.51 ± 0.53 | 12.94 ± 0.00 | 8.33 ± 0.00 | 7.48 ± 0.05 | 7.42 ± 0.07 | ||
| δ = 0.05 | Add. | 1.00 ± 0.13 | 1.05 ± 0.18 | 1.04 ± 0.21 | 1.04 ± 0.17 | 16.72 ± 0.00 | 12.45 ± 0.00 | 12.56 ± 0.02 | 12.26 ± 0.02 | |
| Mult. | 1.01 ± 0.13 | 1.05 ± 0.18 | 1.04 ± 0.20 | 1.03 ± 0.16 | 16.76 ± 0.00 | 12.61 ± 0.00 | 13.21 ± 0.08 | 12.75 ± 0.12 | ||
| RCPS | δ = 0.20 | Add. | 2.01 ± 0.20 | 2.05 ± 0.30 | 2.06 ± 0.33 | 2.06 ± 0.30 | 14.87 ± 0.00 | 10.05 ± 0.00 | 9.47 ± 0.02 | 9.35 ± 0.02 |
| Mult. | 2.01 ± 0.20 | 2.05 ± 0.30 | 2.06 ± 0.33 | 2.05 ± 0.28 | 14.90 ± 0.00 | 10.15 ± 0.00 | 9.90 ± 0.06 | 9.71 ± 0.09 | ||
| δ = 0.50 | Add. | 3.00 ± 0.25 | 3.06 ± 0.41 | 3.08 ± 0.45 | 3.07 ± 0.41 | 13.79 ± 0.00 | 8.96 ± 0.00 | 7.91 ± 0.02 | 7.88 ± 0.02 | |
| Mult. | 3.01 ± 0.25 | 3.06 ± 0.40 | 3.09 ± 0.45 | 3.06 ± 0.39 | 13.80 ± 0.00 | 9.03 ± 0.00 | 8.30 ± 0.05 | 8.23 ± 0.07 | ||
Note. The metrics are computed for each mass mapping method, before and after calibration, for various error levels δ (RCPS only), and various families of calibration functions (gλ)λ. “Add.” and “Mult.” refer to the families defined in Eqs. (49) and (50), respectively, whereas “χ2” refers to the chi-squared family defined in Eq. (51), with k = 3 degrees of freedom. The multiplicative factor b, which depends on the scaling factor a, is set to the maximum value such that gλ remains non-decreasing for any λ ≥ 0. “KS1” and “KS2” correspond to the KS estimators with weak and strong smoothing, respectively. The miscoverage rate (35) as well as the length of the prediction intervals are averaged over the set ℳ of active pixels, for each pair (γi, κi). The empirical mean and standard deviation of each metric is then computed over the test set (γi, κi)i = n + 1m, and displayed in this table.
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