Sampling decomposable graphs using a Markov chain on junction trees

Sampling decomposable graphs using a Markov chain on junction trees

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...

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Veröffentlicht in:Biometrika 2013-03, Vol.100 (1), p.91-110
Hauptverfasser: GREEN, PETER J., THOMAS, ALUN
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Sprache:eng
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Bayesian analysis
Geometry
Graph theory
Graphs
Markov analysis
Monte Carlo simulation
Studies
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description 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 chain Monte 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.
doi_str_mv 10.1093/biomet/ass052
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source JSTOR Mathematics & Statistics; Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current); Alma/SFX Local Collection
subjects Bayesian analysis
Geometry
Graph theory
Graphs
Markov analysis
Monte Carlo simulation
Studies
title Sampling decomposable graphs using a Markov chain on junction trees
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