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

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  • Peter J Green
  • Alun Thomas

Abstract

Summary 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.

Suggested Citation

  • Peter J Green & Alun Thomas, 2018. "A structural Markov property for decomposable graph laws that allows control of clique intersections," Biometrika, Biometrika Trust, vol. 105(1), pages 19-29.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:19-29.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx072
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    References listed on IDEAS

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    1. Peter J. Green & Alun Thomas, 2013. "Sampling decomposable graphs using a Markov chain on junction trees," Biometrika, Biometrika Trust, vol. 100(1), pages 91-110.
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    Cited by:

    1. Xiong Kang & Yingying Hu & Yi Sun, 2023. "Undirected Structural Markov Property for Bayesian Model Determination," Mathematics, MDPI, vol. 11(7), pages 1-22, March.

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