Top panels: Marginalized posterior density distribution of D_d, based on the joint models using ideal kinematic data. The different colors represent posterior densities corresponding to different BH masses, while each color represents five separate posterior distributions that are tightly clustered together, corresponding to models with identical mass parameterizations but different source-grid resolutions. The red color represents EPL mass models, where a small softening scale of r_soft = 0.01″ mimics the presence of a massive BH, eliminating the need to explicitly include an additional M_BH. The left panel shows equally weighted D_d posterior densities, whereas the right panel presents the combined D_d posterior density weighted by BIC (see Sect. 3.4). Bottom panels: Marginalized posterior density distribution of D_Δt, int, based on joint models using ideal kinematic data. The red dashed lines in both panels indicate the mock input values used in the simulated data. The black dashed lines represent the median values in the BIC-weighted distribution.