For all continuous shrinkage priors that take the general form in Eq. (6), Gibbs samplers with block update of the regression coefficients β (i.e., SNP effect sizes) can be easily derived. By using LD information from an external reference panel, the method can be applied to GWAS summary statistics and does not require individual-level data. We describe the Gibbs sampler in Supplementary Note. In this study, we focus on a specific set of parameter values of the gamma-gamma prior on ψj (or equivalently, the TPB prior on τj): a = 1 and b = 1/2. This particular specification is known as the Strawderman-Berger prior17,18 or the quasi-Cauchy prior51, and appears to work well across a range of simulated and real genetic architectures.
