Some examples of the conditional exponential models

Abstract

Graphical models have widely been used in a variety of research fields due to easiness of interpretation of the model and of model representation via graph. The graphical Gaussian model, a particular version of graphical model, as introduced by Speed and Kiiveri (1986) results from covariance selection models defined by Dempster(1972). Also, graphical models for mixed discrete and continuous variables were introduced by Lauritzen and Wermuth(1989). In this thesis, we expand the concept of conditional Gaussian model to the exponential family, and explored maximum likelihood estimators of conditional Exponential models. These maximum likelihood estimators are illustrated through some examples.