University of Washington - Department of Statistics
Advisor: Thomas Richardson
Graphical models provide an intuitive way of representing conditional independence relations over multivariate distributions. We work with a very general class of graphs we dub Mixed Euphonious Graphs (MEGs), which include DAGs, undirected graphs and ancestral graphs as special cases. Markov properties and parametrizations of discrete distributions obeying the global Markov property for MEGs were found by Richardson (2003, 2009). We discuss this parametrization, and a Maximum Likelihood fitting algorithm which uses it.
The marginal log-linear parameters of Bergsma and Rudas (2002) give variation independent parametrizations for some discrete models; we show how to parametrize discrete MEG models in this spirit, and characterize when this parametrization is variation independent. This parametrization has some nice features, which we discuss. We also demonstrate how the potentially slow Iterative Proportional Fitting algorithm may be avoided in the case of binary models.