On the relation between conditional independence models determined by finite distributive lattices and by directed acyclic graphs

DOI10.1016/0378-3758(94)00150-TzbMath0839.62063OpenAlexW1973266851MaRDI QIDQ1907644

Christopher M. Triggs, Michael D. Perlman, David Madigan, Steen Arne Andersson

Publication date: 19 June 1996

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(94)00150-t

zbMATH Keywords

posetpartially ordered setMarkov modeldirected acyclic graphstransitiveundirected graphsacyclicfinite distributive latticesjoin-irreducible elementdecomposable graphsrecursive factorizationMarkov equivalentmultivariate conditional independence modelspositive joint densitiestransitive DAG models

Mathematics Subject Classification ID

Multivariate analysis (62H99) Applications of graph theory (05C90)

Related Items

A universal algebraic approach for conditional independence, A characterization of Markov equivalence classes for acyclic digraphs, Groups acting on Gaussian graphical models, A characterization of moral transitive acyclic directed graph Markov models as labeled trees., Comments on: Sequences of regressions and their independences, Lattice conditional independence models and Hibi ideals, Totally ordered conditional independence models, Conjunctive Bayesian networks, Conditional independence models for seemingly unrelated regressions with incomplete data, Wishart distributions on homogeneous cones, Inadmissibility of the maximum likelihood estimator of normal covariance matrices with the lattice conditional independence, Symmetry and lattice conditional independence in a multivariate normal distribution, Normal linear regression models with recursive graphical Markov structure, Lattice conditional independence models for contingency tables with non-monotone missing data patterns, Lattice conditional independence models for seemingly unrelated regressions, Invariant normal models with recursive graphical Markov structure., Ancestral graph Markov models.

Cites Work

• The EM algorithm for graphical association models with missing data
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• Lattice-ordered conditional independence models for missing data
• Hyper Markov laws in the statistical analysis of decomposable graphical models
• Lattice models for conditional independence in a multivariate normal distribution
• Bayesian analysis in expert systems. With comments and a rejoinder by the authors
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• Graphical and Recursive Models for Contingency Tables
• Linear Recursive Equations, Covariance Selection, and Path Analysis
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