The Annals of Statistics

Ancestral graph Markov models

Peter Spirtes and Thomas Richardson

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist. Volume 30, Number 4 (2002), 962-1030.

Dates
First available in Project Euclid: 10 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1031689015

Digital Object Identifier
doi:10.1214/aos/1031689015

Mathematical Reviews number (MathSciNet)
MR1926166

Zentralblatt MATH identifier
1033.60008

Subjects
Primary: 62M45: Neural nets and related approaches 60K99: None of the above, but in this section
Secondary: 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35] 68T30: Knowledge representation

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

Citation

Richardson, Thomas; Spirtes, Peter. Ancestral graph Markov models. Ann. Statist. 30 (2002), no. 4, 962--1030. doi:10.1214/aos/1031689015. http://projecteuclid.org/euclid.aos/1031689015.


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