Dispersion outliers For some genes, the gene-wise estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\alpha ^{\text {gw}}_{i}$ \end{document}αigw can be so far above the prior expectation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\alpha _{\text {tr}}(\bar \mu _{i})$ \end{document}αtr(μ¯i) that it would be unreasonable to assume that the prior is suitable for the gene. If the dispersion estimate for such genes were down-moderated toward the fitted trend, this might lead to false positives. Therefore, we use the heuristic of considering a gene as a dispersion outlier, if the residual from the trend fit is more than two standard deviations of logarithmic residuals, slr (see Equation (8)), above the fit, i.e., if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \log \alpha_{i}^{\text{gw}} > \log\alpha_{\text{tr}}(\bar\mu_{i}) + 2 s_{\text{lr}}. $$ \end{document}logαigw>logαtr(μ¯i)+2slr.
