Violin plots for the LVG-MCMC-derived posterior distributions of n_H2, T_kin, and N_mol/dV in APM 08279+5255 and NCv1.143 (upper and lower panels, respectively). The white dot represents the median values, while the solid blue and dashed blue lines represent ±1σ and ±2σ, respectively. The violin shapes represent the posterior distributions of each parameter as presented in the corner plots (Figs. B.1 and B.2).