We consider a Bayesian high-dimensional regression framework for polygenic modeling and prediction:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{y}}_{N \times 1} = {\mathbf{X}}_{N \times M}{\boldsymbol{\beta }}_{M \times 1} + {\boldsymbol{\varepsilon}} _{N \times 1},$$\end{document}yN×1=XN×MβM×1+εN×1,where N and M denote the sample size and number of genetic markers, respectively, y is a vector of traits, X is the genotype matrix, β is a vector of effect sizes for the genetic markers, and ε is a vector of residuals. By assigning appropriate priors on the regression coefficients β to impose regularization, additive PRS can be calculated using posterior mean effect sizes.
