Table 2.
Inference on the hyper-parameters of the extended model given mock data from a sample of 1000 strong lenses.
| Parameter | Truth | Prior | Full data | Image pos. only | Description |
|---|---|---|---|---|---|
| μDM, 0 | 11.05 | U(10.00, 12.00) |
 |
 |
Mean log MDM, 5 at  and average size |
| βDM | 0.60 | U(0.00, 3.00) |
 |
 |
Dependence of log MDM, 5 on  |
| ξDM | −0.21 | U(−1.00, 1.00) |
 |
 |
Dependence of log MDM, 5 on galaxy size |
| σDM | 0.06 | U(0.02, 0.50) |
 |
 |
Intrinsic scatter in log MDM, 5 |
| μγ, 0 | 1.47 | U(0.80, 1.80) |
 |
 |
Mean γDM at  and average size |
| βγ | −0.41 | U(−1.00, 1.00) |
 |
 |
Dependence of γDM on  |
| ξγ | −0.34 | U(−1.00, 1.00) |
 |
 |
Dependence of γDM on galaxy size |
| σγ | 0.06 | U(0.02, 0.50) |
 |
 |
Intrinsic scatter in γDM |
| log αsps | 0.10 | U(0.00, 0.25) |
 |
 |
Log of the stellar population synthesis mismatch parameter |
Notes. Column (2): true values of the hyper-parameters. For the hyper-parameters relative to the inner dark matter slope, these are defined by fitting the model directly to the distribution of MDM, 5 and γDM. Column (3): priors on the hyper-parameters. Columns (4) and (5): median, 16th and 84th percentile of the marginal posterior probability distribution of each hyper-parameter given the full dataset (image positions and radial magnification ratios) and image position data only.
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