ABSTRACT
The chapter introduces the Chain Event Graph (CEG) as a new graphical statistical model based on an event tree. It outlines how the probability tree can be used as a graphical representation of a certain probability space, and how an additional colouring of this tree can capture implicit conditional independence assumptions associated to the depicted events. The chapter utilizes the staged tree semantics for proving more technical results. It investigates the class of CEG models in relation to other established classes of graphical models. The chapter introduces some notation from graph theory which enables us to discuss discrete and parametric statistical models represented by probability trees. It provides expressive illustrations to the concepts introduced and to develop the CEG as a graphical model based on a probability tree. Square-free CEGs have turned out to be extremely important. For instance, equivalence classes of square-free CEGs representing the same statistical model can be determined in a straightforward way.
