Statistics – Computation
Scientific paper
2011-04-20
Statistics
Computation
21 pages, 7 figures, 1 table. V2 as V1 except that Fig 1 was corrected. V3 has significant edits, dropping some figures and in
Scientific paper
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. 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 specific models.
Green Peter J.
Thomas Alun
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