Comparison of projected posterior distributions between the baseline constant scatter model and the simulation-derived scatter model for the two parameters of the scaling relation in Eq. (22). The ‘Gaussian A_σ’ refers to the use of scatter-halo mass relation of Eq. (26) with a Gaussian prior for A_σ. The contours represent the 68% and 95% credible intervals, smoothed with a matched elliptical Gaussian kernel density estimator.