Examples of an inlier (orange) and an outlier (purple) PDF (left panel). By definition, the point estimate derived for the two sources from the main mode falls within or outside the grey shaded region. Both sources show a secondary peak in the PDF. We can define the probability of being an inlier (colored area under the PDF which coincides with the grey shaded area). Normalized $\frac{\left|\mathrm{\Delta }Z\right|}{\left(1+z_{\text{spec\hspace{0.17em}}}\right)}$ as a function of inlier probability, color-coded by number density (right panel). The majority of the inliers have a high inlier probability, indicating the stability of our results (see main text for details).