the other regions (mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat r_b = 0.89$$\end{document}r^b=0.89 and s.e. = 0.006) were significantly smaller than the pairwise correlations between the other regions (mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat r_b = 0.98$$\end{document}r^b=0.98 and s.e. = 0.003). We performed the same analysis in the Braineac data and observed similar results as above (Supplementary Fig. 5). The estimates of rb between brain and blood in GTEx varied from 0.74 to 0.79 across different brain regions with a mean estimate of 0.77 (s.e. = 0.010), similar to the mean estimate of local rg between GTEx-blood and 10 other non-brain GTEx tissues reported in a previous study14. The estimate of rb between CMC (brain) and GTEx-blood was 0.74 (s.e. = 0.014), suggesting that the between-sample genetic heterogeneity is small, in line with the strong correlations between CMC and GTEx brain regions (mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat r_b = 0.87$$\end{document}r^b=0.87 and s.e. = 0.010). The estimates of rb from ROSMAP were remarkably similar to those from CMC, providing an important replication of the result. The correlations related to Braineac were notably lower than those related
