Statistics – Other Statistics
Scientific paper
2011-10-19
Statistics
Other Statistics
29 pages, 14 figures, 1 table
Scientific paper
In this paper we study classes of graphs with three types of edge that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the $m$-separation criterion. These include MC, summary, and ancestral graphs. As a modification of MC graphs we define the class of ribbonless graphs (RGs) that permits the use of the $m$-separation criterion. RGs contain summary and ancestral graphs as subclasses, and each RG can be generated by a DAG after marginalisation and conditioning. We derive simple algorithms to generate RGs, from given DAGs or RGs, and also to generate summary and ancestral graphs in a simple way by further extension of the RG-generating algorithm. This enables us to develop a parallel theory on these three classes and to study the relationships between them as well as the use of each class.
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