Posterior probability distributions for the model parameters from the validation exercise. The vertical and horizontal lines show the input values used to generate the synthetic spectra: n_e = 10 cm⁻³, T_e = 8000 K, EM = 1000 pc cm⁻⁶, f_bg = 0.44, and f_m = 5.5 × 10⁻⁴. f_m represents the fraction of the observed continuum that is nonthermal and comes from the same volume as the HRRLs. The blue dotted line shows the case where all model parameters are free, and f_m can take values between 10⁻⁴ and 10⁻²; the dark red solid line shows the case where f_m = L/D_gal; the green dashed line shows the case where f_m = L/D and f_bg = (D_gal − D)/D_gal; and the red dotted–dashed line shows the case where f_m = L/D, f_bg = (D_gal − D)/D_gal, and a Gaussian prior for the electron temperature is adopted.