Distribution of the different fit statistics for synthetic cluster samples. From left to right, the columns correspond to ${\chi }_{\text{red}}^2,D_{\text{KL}}$, D_KL, and E[ln P], respectively. The three topmost rows show the distribution for the base model, including binned 2D distributions. The contour lines enclose 11.8%, 39.3%, 67.5% and 86.4% of samples. This corresponds to levels of 0.5σ, 1σ, 1.5σ, and 2σ for a 2D Gaussian. Samples outside the contours are drawn as individual dots. The bottom row contains histograms for samples of the χ²-fit, D_KL-fit, and E[ln P]-fit models. The blue lines mark the values of the fit statistics for the observed sample listed in Table 5.