Graphical Gaussian models with edge and vertex symmetries

Journal article

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. © 2008 Royal Statistical Society.

Authors: Hojsgaard, S; Lauritzen, S

• Publication status: Published
• Journal: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• Volume: 70
• Issue: 5
• Pages: 1005-1027
• Publication date: 2008-11-01
• DOI: 10.1111/j.1467-9868.2008.00666.x
• EISSN: 1467-9868
• ISSN: 1369-7412
• Language: English
• Keywords: Patterned covariance matrices; Transformation models; Covariance selection; Permutation symmetry; Iterative partial maximization; Invariance; Conditional independence