We find that the predictive performance of the model is not sensitive to the global shrinkage parameter ϕ, and setting ϕ1/2 roughly to the proportion of causal variants52 works well. If a prior guess of the sparseness of the genetic architecture is not available, we provide two ways to learn ϕ. In PRS-CS, we search a small number of ϕ values: ϕ1/2 ∈ {0.0001, 0.001, 0.01, 0.1, 1}, and select the ϕ that produces the best predictive performance in a validation data set, which is independent of the testing set where prediction accuracy of the algorithm is evaluated. In PRS-CS-auto, we use a fully Bayesian approach and assign a standard half-Cauchy prior on ϕ1/219,20, such that ϕ is automatically learnt from GWAS summary statistics and no validation data set is needed. See Supplementary Note for the Gibbs updates of ϕ.
