Bernoulli

  • Bernoulli
  • Volume 19, Number 5B (2013), 2330-2358.

Stable mixed graphs

Kayvan Sadeghi

Full-text: Open access

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 $m$-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.

Article information

Source
Bernoulli, Volume 19, Number 5B (2013), 2330-2358.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078605

Digital Object Identifier
doi:10.3150/12-BEJ454

Mathematical Reviews number (MathSciNet)
MR3160556

Zentralblatt MATH identifier
1317.05077

Keywords
ancestral graph directed acyclic graph independence model $m$-separation criterion marginalisation and conditioning MC graph summary graph

Citation

Sadeghi, Kayvan. Stable mixed graphs. Bernoulli 19 (2013), no. 5B, 2330--2358. doi:10.3150/12-BEJ454. https://projecteuclid.org/euclid.bj/1386078605


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