Exploiting the diversity of modeling methods to probe systematic biases in strong lensing analyses

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Volume 692 (December 2024)

A&A, 692 (2024) A87

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Table 2.

Posterior statistics of source and lens properties inferred from the six lens models shown in Fig. 1.

Quantity	r_eff [″] ^(†)	q_s ^(†)	m_s [mag]	θ_E [″]	γ	q_m	ϕ_m	x₀ [″]	y₀ [″]	γ_ext	ϕ_ext [°]
Truth	0.481	0.66	23.2	1.550	2.040	0.82	−10.0	0.040	0.050	0.030	15.0
μ_models	0.487	0.67	23.1	1.551	2.066	0.80	−9.9	0.034	0.047	0.033	13.9
σ_models	0.004	0.02	0.04	0.001	0.009	0.03	2.3	0.005	0.004	0.002	4.6
Max. bias ^(††)	×	×	×	1.7σ	1.6σ	−3.3σ	2.3σ	−5.5σ	−3.7σ	2.7σ	2.2σ

Combined	×	×	×	$1 . 55_{- 0.002}^{+ 0.002}$ $1.55_{-0.002}^{+0.002}$	$2 . 07_{- 0.02}^{+ 0.03}$ $2.07_{-0.02}^{+0.03}$	$0 . 80_{- 0.03}^{+ 0.03}$ $0.80_{-0.03}^{+0.03}$	$- 10 . 5_{- 2.6}^{+ 1.4}$ $-10.5_{-2.6}^{+1.4}$	$0 . 033_{- 0.004}^{+ 0.004}$ $0.033_{-0.004}^{+0.004}$	$0 . 046_{- 0.005}^{+ 0.004}$ $0.046_{-0.005}^{+0.004}$	$0 . 032_{- 0.003}^{+ 0.003}$ $0.032_{-0.003}^{+0.003}$	$13 . 8_{- 4.5}^{+ 3.3}$ $13.8_{-4.5}^{+3.3}$
Bias ^(††)	×	×	×	0.3σ	1.2σ	−0.6σ	−0.2σ	−1.6σ	−0.9σ	0.7σ	−0.3σ

Notes. In the second and third row μ_model and σ_model show the average and standard deviation of the posterior means of all models, respectively. The fourth row gives the maximal bias among all models for each lens potential parameter. The two last rows correspond to the combined posterior distribution shown in black in Fig. 6.

^(†)

The source properties correspond to best-fit models, whereas lens properties relate to the corresponding marginalized posterior distributions shown in Fig. 6 (individual and combined models). Note that we do not provide combined estimates for the source properties as we do not have formal posterior distributions not uncertainty estimations for all source models.

^(††)

The maximum bias among all models is based on the difference between the mean posterior value and the true value, in units of the posterior standard deviation (negative and positive biases correspond to under- or over-estimates, respectively). The last row of the table shows the corresponding bias value from the combined posterior distribution.

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