In the first example (Fig. 4, left-hand column), raw effect estimates in each tissue are mostly positive, and strongest in brain tissues. The mash estimates are all positive: the few modest negative estimates are outweighed by the strong background information that effects are highly correlated among tissues and mostly positive. This weighing of evidence was done using Bayes’ rule. Humans are notoriously bad at weighing background information against specific instances—they tend to underweight background information when presented with specific data22—so this behavior may or may not be intuitive. The mash effect estimates are also appreciably larger in brain tissues than in other tissues. This is a result of using Bayes’ rule to combine the effect estimates at this eQTL with the background information on heterogeneity of brain and non-brain effects learned from all eQTLs.
