Graphical Gaussian models with edge and vertex symmetries

• 成果类型: Article
• 署名作者: Hojsgaard, Soren; Lauritzen, Steffen L.
• 署名单位: University of Oxford; Aarhus University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00666.x
• 发表日期: 2008
• 页码: 1005-1027
• 关键词: spatial interaction; likelihood; selection

摘要

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.