Influence of scatter on the stellar mass – UV luminosity relation. Shown are the conditional probability distributions of the galaxy stellar mass for a fixed UV magnitude ℳ_UV = −20 when including scatter in the stellar mass – halo mass and UV luminosity – halo mass relations, calculated using Equation (B.7) for a fixed set of model parameter. The grey line shows the probability distribution when assuming log M_⋆ and log L_UV are distributed according to a Gaussian distribution with σ_M⋆ = 0.05 and σ_LUV = 0.25. The pink line assumes a skew-normal distribution (a generalisation of the normal distribution that allows for non-zero skewness) for L_UV with a skewness parameter α = −40. All distributions have a median given by Equation (2). The black vertical line shows the value of M_⋆ calculated without assuming scatter. The scatter influences the location and shape of the distributions, the skewed case produces a distribution that more closely matches the observations shown in Figure 8.