We then classified the process-of-origin for each singleton according to the following optimal decision rule:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{k}}_{i,j}={\rm{\arg }}\,{{\rm{\max }}}_{k\in \{1,\mathrm{..}.,4\}}p(k|{d}_{i,j}).$$\end{document}kˆi,j=argmaxk∈{1,...,4}p(k|di,j).
