Now let ki,j indicate which of the four processes generated singleton j in individual i. We calculated the probability of being generated by process k as:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p({k}_{i,j}=k|{d}_{i,j};\,k\in \{1,\mathrm{...},4\})=\frac{p({d}_{i},k)}{p({d}_{i})}=\frac{{\lambda }_{i,k}\,{f}_{k}({d}_{i};{\theta }_{i,k})}{{\sum }_{k=1}^{4}{\lambda }_{i,k}\,{f}_{k}({d}_{i};{\theta }_{i,k})}.$$\end{document}p(ki,j=k|di,j;k∈{1,...,4})=p(di,k)p(di)=λi,kfk(di;θi,k)∑k=14λi,kfk(di;θi,k).
