Table 2
Sample model comparison.
| Sample results | Bootstrapped results | ||||
| Model | # rej | ∑ log Z | # rej | ∑ log Z | ruled out |
| (1) | (2) | (3) | (4) | (5) | (6) |
|
|
|||||
| All (334 sources) | |||||
| torus+pexmon+scattering | 11 | −85.6 | 10 ± 3.4 | −85.4 ± 8.0 | 9 ± 28% |
| wabs+pexmon+scattering | 8 | −93.4 | 8 ± 2.7 | −93.6 ± 7.6 | 85 ± 35% |
| sphere+pexmon+scattering | 11 | −95.3 | 10 ± 3.3 | −95.1 ± 7.8 | 100 ± 5% |
| torus+scattering | 16 | −116.8 | 16 ± 4.0 | −117.3 ± 11.8 | 100 ± 0% |
| sphere+scattering | 21 | −127.3 | 21 ± 4.6 | −127.3 ± 10.3 | 100 ± 0% |
| wabs+scattering | 37 | −167.6 | 37 ± 5.7 | −168.6 ± 14.2 | 100 ± 0% |
| torus | 39 | −188.2 | 39 ± 5.9 | −190.4 ± 20.0 | 100 ± 0% |
| sphere | 55 | −233.1 | 55 ± 6.8 | −235.3 ± 22.3 | 100 ± 0% |
| wabs | 59 | −270.9 | 59 ± 6.8 | −274.1 ± 26.9 | 100 ± 0% |
| powerlaw | 187 | −2657.9 | 186 ± 9.6 | −2704.8 ± 412.6 | 100 ± 0% |
|
|
|||||
| log NH = 20−22 (54 sources) | |||||
| wabs+pexmon+scattering | 2 | −24.0 | 2 ± 1.3 | −24.4 ± 5.1 | 54 ± 50% |
| sphere+pexmon+scattering | 2 | −24.4 | 2 ± 1.3 | −24.9 ± 5.3 | 63 ± 48% |
| powerlaw | 7 | −24.9 | 7 ± 2.7 | −25.2 ± 9.4 | 44 ± 50% |
|
|
|||||
| log NH = 22−23 (47 sources) | |||||
| torus+pexmon+scattering | 0 | −5.3 | 0 ± 0.0 | −5.2 ± 0.7 | 0 ± 0% |
| sphere+pexmon+scattering | 0 | −6.6 | 0 ± 0.0 | −6.5 ± 0.7 | 70 ± 46% |
| wabs+pexmon+scattering | 0 | −7.5 | 0 ± 0.0 | −7.5 ± 0.7 | 98 ± 14% |
| torus+scattering | 3 | −13.1 | 2 ± 1.6 | −12.6 ± 3.5 | 98 ± 14% |
|
|
|||||
| log NH = 23−24 (51 sources) | |||||
| wabs+pexmon+scattering | 0 | −10.1 | 0 ± 0.0 | −10.1 ± 1.1 | 6 ± 24% |
| torus+pexmon+scattering | 4 | −12.6 | 3 ± 1.8 | −12.4 ± 2.2 | 67 ± 47% |
|
|
|||||
| log NH = 24−26 (14 sources) | |||||
| torus+scattering | 0 | −1.5 | 0 ± 0.0 | −1.5 ± 0.5 | 7 ± 26% |
| torus+pexmon+scattering | 0 | −1.7 | 0 ± 0.0 | −1.7 ± 0.3 | 7 ± 26% |
| torus | 3 | −9.8 | 3 ± 2.1 | −10.3 ± 7.1 | 93 ± 26% |
|
|
|||||
| log NH = 22−26 (176 sources) | |||||
| torus+pexmon+scattering | 4 | −30.2 | 4 ± 1.9 | −30.0 ± 3.1 | 0 ± 0% |
| wabs+pexmon+scattering | 6 | −46.4 | 6 ± 2.5 | −46.6 ± 5.1 | 99 ± 8% |
|
|
|||||
| z > 1 (229 sources) | |||||
| torus+pexmon+scattering | 8 | −57.6 | 8 ± 3.0 | −58.9 ± 7.7 | 11 ± 32% |
| wabs+pexmon+scattering | 5 | −64.5 | 5 ± 2.3 | −65.2 ± 7.7 | 80 ± 40% |
| torus+scattering | 7 | −67.7 | 7 ± 2.5 | −68.5 ± 7.7 | 100 ± 7% |
|
|
|||||
| z > 2 (96 sources) | |||||
| torus+pexmon+scattering | 4 | −28.4 | 4 ± 2.0 | −28.8 ± 6.1 | 25 ± 43% |
| torus+scattering | 3 | −30.2 | 2 ± 1.6 | −30.8 ± 6.0 | 75 ± 43% |
| wabs+pexmon+scattering | 2 | −30.8 | 2 ± 1.3 | −31.7 ± 5.9 | 66 ± 47% |
| sphere+scattering | 7 | −39.0 | 7 ± 2.4 | −39.9 ± 5.8 | 99 ± 10% |
Notes. Considering each source in turn, the second column shows in how many sources model comparison ruled out the particular model. The third column shows the total evidence across all sources, relative to the best evidence. The following columns show the same statistics, but using bootstrapping on the sample, making the computed quantities more robust against outliers. The last column computes how often in the bootstrapping the model was ruled out based on the total evidence (10 times less likely than other models). In the lower table segments, the sample is split by log NH, estimated using the 90% quantiles of the torus+scattering model posterior. Models with mean 100% and root mean square 0% in Col. 6 are not shown in the lower segments.
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