Chunk #48 — Methods — Simulation description

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scCODA is a Bayesian model for compositional single-cell data analysis.

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The sets of generation parameters were as follows:Model comparison (Fig. 2, Methods—“Model comparison”):\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=\{5,10,15\};$$\end{document}K={5,10,15};\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n}_{0}={n}_{1}=\{1,2,3,4,5\}({{{{{\mathrm{only}}}}}}\,{{{{{\mathrm{balanced}}}}}}\,{{{{{\mathrm{setups}}}}}}-{n}_{0}={n}_{1});$$\end{document}n0=n1={1,2,3,4,5}(onlybalancedsetups−n0=n1);\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{y}=K\cdot 1000;$$\end{document}ȳ=K⋅1000;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{0}=1000;$$\end{document}μ0=1000;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{\boldsymbol{\mu }}}}}}}^{\prime}=(0,500);(0,1000);(0,2000);(500,1000);(500,2000);(1000,2000);$$\end{document}μ′=(0,500);(0,1000);(0,2000);(500,1000);(500,2000);(1000,2000);\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=20;$$\end{document}r=20;Power analysis (Supplementary Fig. 4, Methods—“Power analysis”):\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=5;$$\end{document}K=5;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n}_{0}={n}_{1}=\{1,2,{{{{\mathrm{..}}}}}.,10\}({{{{{\mathrm{also}}}}}}\,{{{{{\mathrm{imbalanced}}}}}}\,{{{{{\mathrm{setups}}}}}});$$\end{document}n0=n1={1,2,...,10}(alsoimbalancedsetups);\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{y}=5000;$$\end{document}ȳ=5000;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{0}=\{20,30,50,75,115,180,280,430,667,1000\};$$\end{document}μ0={20,30,50,75,115,180,280,430,667,1000};\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{\boldsymbol{\mu }}}}}}^{\prime} =\{10,20,30,40,50,60,70,80,90,100,200,400,600,800,1000\};$$\end{document}μ′={10,20,30,40,50,60,70,80,90,100,200,400,600,800,1000};\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=10;$$\end{document}r=10;Heterogeneous response groups (Supplementary Fig. 9, Methods—“Analysis of heterogeneous response groups”):\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=5;$$\end{document}K=5;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n}_{0}={n}_{1}=20;$$\end{document}n0=n1=20;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{y}=5000;$$\end{document}ȳ=5000;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{0}=\{1,100,1000\};$$\end{document}μ0={1,100,1000};\documentclass[12pt]{minimal}