its effect size βjk, which can be represented as global-local scale mixtures of normals: βjk~N(0,σk2Nkψj), ψj~Gamma(a,δj), δj~Gamma(b,ϕ), where ϕ is a global shrinkage parameter shared across all SNPs that models the overall sparseness of the genetic architecture, and Ψj is a local, SNP-specific shrinkage parameter that is adaptive to marginal GWAS associations. By assigning a gamma-gamma hierarchical prior on Ψj (specifically, the Strawderman-Berger prior with a = 1 and b = 1/2 in this work), the marginal prior density of βjk has sizable amount of mass near zero to impose strong shrinkage on small noisy signals, and in the meantime, heavy Cauchy-like tails to avoid over-shrinkage of truly non-zero effects.
