Empirical prior estimate To obtain values for the empirical prior widths σr for the model coefficients, we again approximate a full empirical Bayes approach, as with the estimation of dispersion prior, though here we do not subtract the expected sampling variance from the observed variance of maximum likelihood estimates. The estimate of the LFC prior width is calculated as follows. We use the standard iteratively reweighted least-squares algorithm [12] for each gene’s model, Equations (1) and (2), to get MLEs for the coefficients \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\beta _{\textit {ir}}^{\text {MLE}}$ \end{document}βirMLE. We then fit, for each column r of the design matrix (except for the intercept), a zero-centered normal distribution to the empirical distribution of MLE fold change estimates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\vec {\beta }^{\text {MLE}}_{r}$ \end{document}β→rMLE.
