Chunk #28 — Methods — Model description
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- scCODA is a Bayesian model for compositional single-cell data analysis.
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- yes
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\usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y \sim {{{{{\rm{DirMult}}}}}}(\phi ,\bar{y})$$\end{document}Y~DirMult(ϕ,ȳ)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log (\phi )={{{{{\boldsymbol{\alpha }}}}}}+X\beta$$\end{document}log(ϕ)=α+Xβ3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha }_{k} \sim {{{{{\rm{N}}}}}}(0,5)\quad \forall k\in [1,{{{{\mathrm{.}}}}}.,K]$$\end{document}αk~N(0,5)∀k∈[1,..,K]4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta =\tau \tilde{\beta }$$\end{document}β=τβ~5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tau }_{m,k}=\frac{\exp ({t}_{m,k})}{1+\exp ({t}_{m,k})}\forall m\in [1,\ldots ,M],\,\forall k\in [1,\ldots ,K]$$\end{document}τm,k=exp(tm,k)1+exp(tm,k)∀m∈[1,…,M],∀k∈[1,…,K]6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{t}_{m,k}}{50} \sim {{{{{\rm{N}}}}}}(0,1)\,\forall m\in [1,\ldots ,M],\,\forall k\in [1,\ldots ,K]$$\end{document}tm,k50~N(0,1)∀m∈[1,…,M],∀k∈[1,…,K]7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tilde{\beta }}_{m,k}={\sigma }^{2}{\gamma }_{m,k}\forall m\in [1,{{{{\mathrm{.}}}}}.,M],\,\forall k\in [1,{{{{\mathrm{.}}}}}.,K]$$\end{document}β~m,k=σ2γm,k∀m∈[1,..,M],∀k∈[1,..,K]8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{m}^{2} \sim {{{{{\rm{HC}}}}}}(1)\forall m\in [1,{{{{\mathrm{.}}}}}.,M]$$\end{document}σm2~HC(1)∀m∈[1,..,M]9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\gamma }_{m,k} \sim {{{{{\rm{N}}}}}}(0,1)\forall m\in [1,{{{{\mathrm{.}}}}}.,M],\forall k\in [1,{{{{\mathrm{.}}}}}.,K]$$\end{document}γm,k~N(0,1)∀m∈[1,..,M],∀k∈[1,..,K]with N describing a Normal and HC a Half-Cauchy distribution following Polson et al.’s suggesting of hyperpriors for global scale parameters31.
