Parameters s₀ and (top and bottom, respectively) for a Gaussian conditional sparsity distribution, ρ_s(s_200,500|M_500,c). These parameters are obtained for the distribution that jointly solves the inward, Eq. (4), and outward, Eq. (5), reconstructions assuming two HMF models: Despali et al. (2016) (purple) and using the HMF measured from the simulation data (orange). A comparison of the parameters to the sample mean and variance measured from the data (black lines) shows that s₀ is only accurate to a few percent at recovering the sample mean; this error is carried into the variance, which deviates significantly from the simulation data.