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Undirected Structural Markov Property for Bayesian Model Determination

Author

Listed:
  • Xiong Kang

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China)

  • Yingying Hu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China)

  • Yi Sun

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China)

Abstract

This paper generalizes the structural Markov properties for undirected decomposable graphs to arbitrary ones. This helps us to exploit the conditional independence properties of joint prior laws to analyze and compare multiple graphical structures, while being able to take advantage of the common conditional independence constraints. This work provides a theoretical support for full Bayesian posterior updating about the structure of a graph using data from a certain distribution. We further investigate the ratio of graph law so as to simplify the acceptance probability of the Metropolis–Hastings sampling algorithms.

Suggested Citation

  • Xiong Kang & Yingying Hu & Yi Sun, 2023. "Undirected Structural Markov Property for Bayesian Model Determination," Mathematics, MDPI, vol. 11(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1590-:d:1107060
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    References listed on IDEAS

    as
    1. 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.
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