Let the precision w i denote the inverse of the variance of the observation y i for the i th observation. The precisions can be used to re-weight the samples in a regression to account for the variation in the uncertainty about each observation. Weighting by the precision upweights samples with low measurement error and down weights samples with high measurement error. Denoting the vector of precision weights for a single gene across all samples as w, the model is fit by weighting the residual variance from equation (8) 22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{array}{@{}rcl@{}} \varepsilon &\sim& \mathcal{N}(0, \text{diag}(w)\sigma^{2}_{\varepsilon}). \end{array} $$ \end{document}ε∼N(0,diag(w)σε2).
