Table 1
Performance of inference methods on a synthetic case.
| Estimator | τd | Mean error factor | Runtime | |||||
|---|---|---|---|---|---|---|---|---|
| κ | Pth | G0 | ![$\[A_{V}^{\text {tot}}\]$](/articles/aa/full_html/2025/06/aa54266-25/aa54266-25-eq34.png) |
Total | Per iter. | |||
| Nside = 10 | MLE (le) | − | 1.9 | 31.1 | 56.9 | 3.1 | 4m 09s | 0.06s |
| MLE (ge) | − | 1.6 | 2.3 | 15.6 | 2.8 | 5m 11s | 0.06s | |
| MAP (ge) | 10−1 | 1.4 | 1.8 | 11.8 | 2.1 | 5m 24s | 0.07s | |
| MAP (ge) | 100 | 1.1 | 1.4 | 1.4 | 1.3 | 5m 27s | 0.07s | |
| MAP (ge) | 101 | 1.1 | 1.3 | 1.4 | 1.5 | 5m 21s | 0.06s | |
| MAP (ge) | 102 | 1.5 | 4.7 | 2.2 | 4.8 | 4m 50s | 0.06s | |
| MMSE (ge) | 1.1 | 1.1 | 1.5 | 1.9 | 1.3 | 27m 49s | 0.17s | |
| Nside = 30 | MLE (le) | − | 2.3 | 20.2 | 1231 | 2.9 | 24m 17s | 0.29s |
| MLE (ge) | − | 1.7 | 2.4 | 31.4 | 2.9 | 29m 48s | 0.36s | |
| MAP (ge) | 10−1 | 1.4 | 2.0 | 9.5 | 2.1 | 31m 45s | 0.38s | |
| MAP (ge) | 100 | 1.2 | 1.7 | 3.2 | 1.6 | 31m 21s | 0.38s | |
| MAP (ge) | 101 | 1.2 | 1.3 | 1.3 | 1.3 | 34m 14s | 0.41s | |
| MAP (ge) | 102 | 1.2 | 1.5 | 1.5 | 1.5 | 32m 14s | 0.39s | |
| MMSE (ge) | 4.7 | 1.2 | 1.3 | 1.4 | 1.3 | 2h 09m 44s | 0.78s | |
| Nside = 90 | MLE (le) | − | 2.3 | 21.4 | 1223 | 3.0 | 3h 01m 23s | 2.18s |
| MLE (ge) | − | 1.7 | 2.4 | 22.8 | 2.8 | 4h 53m 46s | 3.53s | |
| MAP (ge) | 10−1 | 1.5 | 2.6 | 32.8 | 2.1 | 6h 10m 57s | 4.45s | |
| MAP (ge) | 100 | 1.3 | 1.6 | 5.5 | 1.6 | 7h 13m 01s | 5.20s | |
| MAP (ge) | 101 | 1.2 | 1.3 | 1.5 | 1.4 | 7h 30m 36s | 5.41s | |
| MAP (ge) | 102 | 1.2 | 1.3 | 1.3 | 1.2 | 6h 15m 13s | 4.50s | |
| MMSE (ge) | 31.1 | 1.1 | 1.3 | 1.3 | 1.3 | 28h 43m 02s | 10.34s | |
Notes. le: local exploration, i.e., with MTM kernel disabled (pMTM = 0). ge: global exploration, i.e., with MTM kernel enabled (pMTM > 0). In each case, the number of pixels in each map is ![$\[N=N_{\text {side }}^{2}\]$](/articles/aa/full_html/2025/06/aa54266-25/aa54266-25-eq35.png)
. The three considered cases thus contain N = 100, 900 and 8100 pixels, respectively. For the MMSE (ge), the regularization weight, τd, is estimated along with the physical parameters, Θ. For each spatial resolution and physical parameter, the lowest mean error factor is highlighted in bold.
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