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Sampling decomposable graphs using a Markov chain on junction trees

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  • Peter J. Green
  • Alun Thomas

Abstract

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs or other special cases, except for small-scale problems, say up to 15 variables. In this paper we develop new, more efficient methodology for such inference, by making two contributions to the computational geometry of decomposable graphs. The first of these provides sufficient conditions under which it is possible to completely connect two disconnected complete subsets of vertices, or perform the reverse procedure, yet maintain decomposability of the graph. The second is a new Markov chainMonte Carlo sampler for arbitrary positive distributions on decomposable graphs, taking a junction tree representing the graph as its state variable. The resulting methodology is illustrated with numerical experiments on three models. Copyright 2013, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:1:p:91-110
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    File URL: http://hdl.handle.net/10.1093/biomet/ass052
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    Cited by:

    1. Yang Ni & Peter Müller & Yitan Zhu & Yuan Ji, 2018. "Heterogeneous reciprocal graphical models," Biometrics, The International Biometric Society, vol. 74(2), pages 606-615, June.
    2. Leonardo Bottolo & Marco Banterle & Sylvia Richardson & Mika Ala‐Korpela & Marjo‐Riitta Järvelin & Alex Lewin, 2021. "A computationally efficient Bayesian seemingly unrelated regressions model for high‐dimensional quantitative trait loci discovery," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 886-908, August.
    3. Guido Consonni & Luca La Rocca & Stefano Peluso, 2017. "Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 741-764, September.
    4. 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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