A structural Markov property for decomposable graph laws that allows control of clique intersections

Peter Green; Alun Thomas

doi:10.1093/biomet/asx072

A structural Markov property for decomposable graph laws that allows control of clique intersections

Peter Green, Alun Thomas

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Abstract

We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.

Original language	English
Pages (from-to)	19-29
Number of pages	11
Journal	Biometrika
Volume	105
Issue number	1
Early online date	11 Dec 2017
DOIs	https://doi.org/10.1093/biomet/asx072
Publication status	Published - 1 Mar 2018

Keywords

Conditional independence
Graphical model
Hub model
Markov random field
Model determination
Random graph

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abstract = "We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.",

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AB - We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.

KW - Conditional independence

KW - Graphical model

KW - Hub model

KW - Markov random field

KW - Model determination

KW - Random graph

U2 - 10.1093/biomet/asx072

DO - 10.1093/biomet/asx072

M3 - Article (Academic Journal)

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JO - Biometrika

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A structural Markov property for decomposable graph laws that allows control of clique intersections

Abstract

Keywords

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