$N(0,\sigma _{\text {d}}^{2})$ \end{document}N(0,σd2) random variables to account for the spread due to the prior. The simulated distribution is shifted by − log(m−p) to account for the scaling of the χ2 distribution. We repeat the simulation over a grid of values for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\sigma _{\text {d}}^{2}$ \end{document}σd2, and select the value that minimizes the Kullback–Leibler divergence from the observed density of logarithmic residuals to the simulated density.
