University of Washington - Department of Statistics
Advisor: Thomas Richardson
Graphical models are an intuitive way to visually represent conditional independence relations over multivariate distributions. We work with acyclic directed mixed graphs (ADMGs), a class which include DAGs and bidirected graphs as special cases.
We present a new parametrization of ADMGs in the case of finite discrete random variables, and see how it can be exploited to produce parsimonious sub-models. We also show that the adaptive lasso is 'oracle' for model selection and parameter estimation with respect to this parametrization; this is illustrated with simulations.
Lastly we discuss the variation dependence properties of the new parametrization, and show that a variation independent parametrization can be constructed for any discrete ADMG model.