Højsgaard, Søren; Lauritzen, Steffen L. Graphical Gaussian models with edge and vertex symmetries. (English) Zbl 1411.62177 J. R. Stat. Soc., Ser. B, Stat. Methodol. 70, No. 5, 1005-1027 (2008). Summary: We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where parameters that are associated with edges or vertices of the same colour are restricted to being identical. We study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation of variable labels. For such models a particularly simple maximization of the likelihood function is available. Cited in 1 ReviewCited in 11 Documents MSC: 62H99 Multivariate analysis 62H12 Estimation in multivariate analysis Keywords:conditional independence; covariance selection; invariance; iterative partial maximization; patterned covariance matrices; permutation symmetry; transformation models Software:gRc PDFBibTeX XMLCite \textit{S. Højsgaard} and \textit{S. L. Lauritzen}, J. R. Stat. Soc., Ser. B, Stat. Methodol. 70, No. 5, 1005--1027 (2008; Zbl 1411.62177) Full Text: DOI