Sampling decomposable graphs using a Markov chain on junction trees

Peter J Green, Alun Thomas

Research output: Contribution to journalArticle (Academic Journal)

21 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)91-110
Number of pages20
JournalBiometrika
Volume100
Issue number1
Early online date28 Jan 2013
DOIs
Publication statusPublished - 2013

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    8092 EPSRC D063485

    Nason, G. P.

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