The mash method uses EB hierarchical modelling, and so is related to other EB methods5,6,12. Indeed, the mash framework essentially includes these methods as special cases (as well as simpler methods such as “fixed effects” and “random effects” meta-analyses9,23). One key feature that distinguishes mash from previous methods is that mash puts greater emphasis on quantitative estimation and assessment of effects. Moving away from binary-based models has at least two advantages. First, allowing for all possible binary configurations can create computational challenges. Second, in practice we have found that effects are often shared broadly among many conditions, and in such cases binary-based methods tend to infer that effects are non-zero in most or all conditions, even when the signal is modest in some conditions. This conclusion may be technically correct—for example, in our GTEx analysis it is not impossible that all eQTLs are somewhat active in all tissues. However, as our analysis has illustrated, a more quantitative focus can reveal variation in effect sizes that may be of considerable biological importance.
