Open Access
August 2002 Ancestral graph Markov models
Thomas Richardson, Peter Spirtes
Ann. Statist. 30(4): 962-1030 (August 2002). DOI: 10.1214/aos/1031689015


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.


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Thomas Richardson. Peter Spirtes. "Ancestral graph Markov models." Ann. Statist. 30 (4) 962 - 1030, August 2002.


Published: August 2002
First available in Project Euclid: 10 September 2002

zbMATH: 1033.60008
MathSciNet: MR1926166
Digital Object Identifier: 10.1214/aos/1031689015

Primary: 60K99 , 62M45
Secondary: 68R10 , 68T30

Keywords: $m$-separation , ancestral graph , DAG , data-generating process , Directed acyclic graph , latent variable , marginalizing and conditioning , MC-graph , path diagram , summary graph

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 4 • August 2002
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