Thomas Richardson
Department of Statistics
Box 354322
University of Washington
Seattle, Washington, 98195
E-mail: tsr@stat.washington.edu
Phone: (206) 685-8488
Fax:(206) 685-7419
Heiko Bailer
Department of Statistics
Box 354322
University of Washington
Seattle, Washington, 98195
E-mail: heiko@stat.washington.edu
Phone: (206) 543-8265
Fax:(206) 685-7419
Moulinath Banarjees
Department of Statistics
Box 354322
University of Washington
Seattle, Washington, 98195
E-mail: mouli@stat.washington.edu
Phone: (206) 543-7237
Fax:(206) 685-7419
The problem of learning the structure of a DAG model in the presence of latent variables presents many formidable challenges. In particular there are an infinite number of latent variable models to consider, and these models possess features which make them hard to work with. We describe a class of graphical models which can represent the conditional independence structure induced by a latent variable model over the observed margin. We give a parametrization of the set of Gaussian distributions with conditional independence structure given by a MAG model. The models are illustrated via a simple example. Different estimation techniques are discussed in the context of Zellner's Seemingly Unrelated Regression (SUR) models.
Multivariate Graphical Models; Causal Modelling; Latent Variables; Ancestral Graphs; MAG Models.