On the basis of the selected genetic effect model (above), for each variant in a locus, we calculated the Bayes factor by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varLambda }_{j}={\rm{\exp }}\left[\frac{{X}_{j}-\left(T+1\right){\rm{\log }}K}{2}\right]$$\end{document}Λj=expXj−T+1logK2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X}_{j}$$\end{document}Xj denotes the chi-squared test statistic for variant j, T denotes the number of axes of genetic variation included in the best-fitting model (that is, 0–4 MDS components) and K denotes the number of studies contributing to the GWAS. Using the approximate Bayes factor, we then calculated the posterior inclusion probability for each variant as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\pi }_{j}=\frac{{\varLambda }_{j}}{{\sum }_{i}{\varLambda }_{i}}$$\end{document}πj=Λj∑iΛi, where i indexes each locus. Finally, we derived 90% credible intervals by ranking variants within a locus by their single posterior estimate and selecting variants until the cumulative posterior inclusion probability reached 0.90.
