Stable mixed graphs
Abstract
In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the -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 -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.
Cite
@article{arxiv.1110.4168,
title = {Stable mixed graphs},
author = {Kayvan Sadeghi},
journal= {arXiv preprint arXiv:1110.4168},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.3150/12-BEJ454 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)