heritability in overlapped annotations, we have βi∼N(0,∑j:i∈Sjτj), where τ0, τ1, …, τK, quantify the contribution to per-SNP heritability from each annotation category. Denote the estimated marginal effect size of the ith SNP as β^i=XiTYN, then we have the following approximation E(Nβ^i2)≈(N−1)∑kτkl(i,k)+1 where l(i, k) is the annotation-stratified LD score and N denotes the total sample size. Regression coefficients τk are estimated through weighted least squares. The estimated heritability of the ith SNP is then Var^(βi)=∑j:i∈Sjτ^j.
