After parameter inference, we calculate the inclusion probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P}_{inc}({\beta }_{k,m})$$\end{document}Pinc(βk,m) of the covariates as follows:10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{c}P({\beta }_{m,k})=\frac{1}{H}\mathop{\sum }\limits_{h=1}^{H}{{{\mathbb{I}}}}(|{\beta }_{m,k,h}|\ge {10}^{-3})\end{array}$$\end{document}P(βm,k)=1H∑h=1HI(∣βm,k,h∣≥10−3)with H the number of HMC iterations and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\mathbb{I}}}}$$\end{document}I the indicator function. To identify credibly associated covariates, we compare the calculated inclusion probabilities with a decision threshold c, which is determined a posteriori to control for the false discovery rate (Methods—“Spike-and-slab threshold determination”). For credible effects, we report the effect parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\beta }_{m,k}$$\end{document}βm,k as the mean over all MCMC samples where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\beta }_{m,k}$$\end{document}βm,k was nonzero.
