Decomposition of ML Estimation in Graphical Models with Koehler Symanowski distributions.
Collaborative Research Center 386, Discussion Paper 105
In the framework of graphical models the graphical representation of the association structure is used in manifold respects. One is the conclusion from a decomposition of the graph to a possible decomposition of the ML estimation. Results are well-known under the assumption of the Conditional Gaussian distribution. Here, graphical models with a family of distributions are considered which is introduced by Koehler and Symanowski (1995). This approach extends the existing theory of graphical models in two respects. The family of distributions we discuss forms an alternative to the usually applied multivariate normal distribution. Furthermore, the focus lies on covariance graphs rather than on concentration graphs. For these models the decomposability of ML estimation is examined.