Final dispersion estimate We form a logarithmic posterior for the dispersion from the Cox–Reid adjusted logarithmic likelihood (7) and the logarithmic prior (5) and use its maximum (i.e., the MAP value) as the final estimate of the dispersion, (9)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \alpha_{i}^{\text{MAP}} = {\underset{\alpha}{\text{arg max}}}\, \left(\ell_{\text{CR}}\left(\alpha; \vec\mu_{\textit{i}\cdot}^{0}, \vec K_{\textit{i}\cdot}\right) + \Lambda_{i}(\alpha) \right), $$ \end{document}αiMAP=arg maxαℓCRα;μ→i·0,K→i·+Λi(α),
