zero to impose strong shrinkage on noise, while at the same time has heavy tails to avoid over-shrinkage of truly non-zero effects. The marker-specific local shrinkage parameter ψj can then adaptively squelch small noisy estimates towards zero, while leaving data-supported large signals unshrunk. In this work, we investigate a specific g (known as the Strawderman-Berger prior17,18; see Methods section), and present two versions of the algorithm, which differ in the way to learn the global scaling parameter ϕ. In PRS-CS, we search a small number of fixed ϕ, select the ϕ value that produces the best predictive performance in a validation data set, and evaluate the algorithm in an independent testing set. In the second version of the algorithm, which we call PRS-CS-auto, we use a fully Bayesian approach and place a standard half-Cauchy prior on the global shrinkage parameter19,20: ϕ1/2 ~ C+(0, 1), such that ϕ is automatically learnt from data and no validation data set is needed.
