Investigating the redshift evolution of lensing galaxy density slopes via model-independent distance ratios

Open Access

Table A.2.

Summary of approaches and results for total mass density, luminous mass density, β prior, cAIC, and BIC values.

Approach	Mass density parameters	β	cAIC	BIC
	$γ_{0}^{EPL - lin} = 2.065 \pm 0.046$ $\rm\gamma_0^{\mathrm{EPL-lin}}=2.065\pm0.046$
Linear evolution + Triangular prior	$γ_{s}^{EPL - lin} = - 0.20 \pm 0.12$ $\rm\gamma_s^{\mathrm{EPL-lin}}=-0.20\pm0.12$	−0.03 ± 0.15	195.70	209.64
Tri(-0.5, 0.656, mode = 0.102)	$δ_{0}^{EPL - lin} = 2.14 \pm 0.16$ $\rm\delta_0^{\mathrm{EPL-lin}}=2.14\pm0.16$
	$δ_{s}^{EPL - lin} = - 0.09 \pm 0.19$ $\rm\delta_s^{\mathrm{EPL-lin}}=-0.09\pm0.19$

	$γ_{0}^{EPL - lin} = 2.054 \pm 0.042$ $\rm\gamma_0^{\mathrm{EPL-lin}}=2.054\pm0.042$
Linear evolution + Gaussian prior	$γ_{s}^{EPL - lin} = - 0.19 \pm 0.11$ $\rm\gamma_s^{\mathrm{EPL-lin}}=-0.19\pm0.11$	0.11 ± 0.13	198.06	212.00
N(μ = 0.22, σ² = 0.2²)	$δ_{0}^{EPL - lin} = 2.26 \pm 0.13$ $\rm\delta_0^{\mathrm{EPL-lin}}=2.26\pm0.13$
	$δ_{s}^{EPL - lin} = - 0.16 \pm 0.18$ $\rm\delta_s^{\mathrm{EPL-lin}}=-0.16\pm0.18$

	$γ_{0}^{EPL - lin} = 2.052 \pm 0.041$ $\rm\gamma_0^{\mathrm{EPL-lin}}=2.052\pm0.041$
Linear evolution + Gaussian prior	$γ_{s}^{EPL - lin} = - 0.19 \pm 0.11$ $\rm\gamma_s^{\mathrm{EPL-lin}}=-0.19\pm0.11$	0.133 ± 0.085	203.60	217.54
N(μ = 0.18, σ² = 0.13²)	$δ_{0}^{EPL - lin} = 2.270 \pm 0.098$ $\rm\delta_0^{\mathrm{EPL-lin}}=2.270\pm0.098$

	$δ_{s}^{EPL - lin} = - 0.18 \pm 0.18$ $\rm\delta_s^{\mathrm{EPL-lin}}=-0.18\pm0.18$
	$γ_{0}^{EPL - ATE} = 2.079 \pm 0.056$ $\rm\gamma_0^{\mathrm{EPL-ATE}}=2.079\pm0.056$
ATE evolution + Triangular prior	$γ_{s}^{EPL - ATE} = - 0.35 \pm 0.23$ $\rm\gamma_s^{\mathrm{EPL-ATE}}=-0.35\pm0.23$	0.02 ± 0.14	196.77	210.71
Tri(-0.5, 0.656, mode = 0.102)	$δ_{0}^{EPL - ATE} = 2.17 \pm 0.17$ $\rm\delta_0^{\mathrm{EPL-ATE}}=2.17\pm0.17$
	$δ_{s}^{EPL - ATE} = - 0.25 \pm 0.40$ $\rm\delta_s^{\mathrm{EPL-ATE}}=-0.25\pm0.40$

	$γ_{0}^{EPL - ATE} = 2.069 \pm 0.051$ $\rm\gamma_0^{\mathrm{EPL-ATE}}=2.069\pm0.051$
ATE evolution + Gaussian prior	$γ_{s}^{EPL - ATE} = - 0.341 \pm 0.23$ $\rm\gamma_s^{\mathrm{EPL-ATE}}=-0.341\pm0.23$	0.12 ± 0.13	208.20	222.14
N(μ = 0.22, σ² = 0.2²)	$δ_{0}^{EPL - ATE} = 2.29 \pm 0.14$ $\rm\delta_0^{\mathrm{EPL-ATE}}=2.29\pm0.14$
	$δ_{s}^{EPL - ATE} = - 0.36 \pm 0.39$ $\rm\delta_s^{\mathrm{EPL-ATE}}=-0.36\pm0.39$

	$γ_{0}^{EPL - ATE} = 2.068 \pm 0.051$ $\rm\gamma_0^{\mathrm{EPL-ATE}}=2.068\pm0.051$
ATE evolution + Gaussian prior	$γ_{s}^{EPL - ATE} = - 0.34 \pm 0.23$ $\rm\gamma_s^{\mathrm{EPL-ATE}}=-0.34\pm0.23$	0.136 ± 0.087	209.11	223.05
N(μ = 0.18, σ² = 0.13²)	$δ_{0}^{EPL - ATE} = 2.30 \pm 0.11$ $\rm\delta_0^{\mathrm{EPL-ATE}}=2.30\pm0.11$
	$δ_{s}^{EPL - ATE} = - 0.34 \pm 0.39$ $\rm\delta_s^{\mathrm{EPL-ATE}}=-0.34\pm0.39$

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