distribution with m−p degrees of freedom, with m the number of samples and p the number of coefficients. The variance of the logarithm of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\chi ^{2}_{f}}$ \end{document}χf2-distributed random variable is given [52] by the trigamma function ψ1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\operatorname{Var} \log X^{2} = \psi_{1}(f/2)\quad\text{for}\quad X^{2} {\sim\chi^{2}_{f}}. $$ \end{document}VarlogX2=ψ1(f/2)forX2∼χf2. Therefore, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\sigma ^{2}_{\text {lde}}\approx \psi _{1}((m-p)/2)$ \end{document}σlde2≈ψ1((m−p)/2), i.e., the sampling variance of the logarithm of a variance or dispersion estimator is approximately constant across genes and depends only on the degrees of freedom of the model.
