LDpred [https://github.com/bvilhjal/ldpred] is a method that infers the posterior mean effect size of each genetic marker from GWAS summary statistics while accounting for LD, using a point-normal prior on the SNP effect sizes and LD information from an external reference panel4. Consider the linear model y = Zβ + ε, where both the phenotype y and the genotype matrix Z have been standardized. LDpred places an independent point-normal prior on each regression coefficient βj:12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _j \sim \left\{ {\begin{array}{*{20}{c}} {N\left( {0,\frac{{h_g^2}}{{\pi M}}} \right),} & {{\mathrm{with}}\,{\mathrm{probability}}\,\pi ,} \\ {\hskip -35pt 0,} & {{\mathrm{with}}\,{\mathrm{probability}}\,1 - \pi ,} \end{array}} \right.$$\end{document}βj~N0,hg2πM,withprobabilityπ,0,withprobability1-π,where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{g}^{2}$$\end{document}hg2 is the heritability explained by genome-wide genetic markers (known as SNP heritability), and π is the fraction of causal variants. Given π and an estimate of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{g}^{2}$$\end{document}hg2, which can be obtained, for example, by applying LD score regression23 to the GWAS summary statistics, LDpred employs an MCMC sampler to approximate the posterior mean of βj, conditioning
