This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.
"Ancestral graph Markov models." Ann. Statist. 30 (4) 962 - 1030, August 2002. https://doi.org/10.1214/aos/1031689015