we have recovered the infinitesimal model16. To create a more flexible model of the genetic architecture, a discrete mixture of two or more point masses or densities can be used, which allows for a wider effect size distribution than a normal prior can produce. For example, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G(\Psi _j) = (1 - \pi )\delta _0 + \pi \delta _{\tau ^2}$$\end{document}G(Ψj)=(1-π)δ0+πδτ2, where π is the mixing probability (the fraction of causal variants), produces the point-normal prior on effect sizes, βj ~ (1−π)δ0 + πN(0, τ2), which was used in LDpred4. Although discrete mixture priors offer a natural and intuitive approach to model non-infinitesimal genetic architectures, posterior inference requires a stochastic search over an exponentially large discrete model space, and does not allow for multivariate block update of effect sizes, which limits computational efficiency and may result in inaccurate modeling of local LD patterns.
