Decomposition of ML Estimation in Graphical Models with Koehler Symanowski distributions

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.