PRS is calculated using the following formula PRS=∑j=1MXjEA(βj|β^,D^), where EA denotes the posterior expectation as described above. In practice, the individual-level genotype matrix is not available and we use the LD matrix estimated from a reference panel or the validation samples to substitute D^. We apply the same standard of choosing the size of b as described in [10]. Choices of prior and p0 can be tuned in an independent cohort. For the data analysis described in this work, we adopted a cross-validation scheme to select tuning parameter due to the challenge in finding multiple independent cohorts without overlapping with the training GWAS summary statistics. The training datasets in our real data analyses and simulations are always fixed, i.e. GWAS summary statistics. We did not perform a classical cross-validation by using different subsets of the complete data to train and test our prediction model. The purpose of cross-validation in our study is purely parameter tuning. To select a suitable tuning parameter, we divide the independent testing dataset (individual level genotype and phenotype data) into two equal parts (A and B),
