Sampling decomposable graphs using a Markov chain on junction trees. (English) Zbl 1284.62172

Green, Peter J.; Thomas, Alun

Biometrika 100, No. 1, 91-110 (2013).

Summary: 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. 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.

MSC:

62F15	Bayesian inference
05C90	Applications of graph theory
65C40	Numerical analysis or methods applied to Markov chains
65C60	Computational problems in statistics (MSC2010)

Keywords:

conditional independence graphs; graphical models; Markov chain Monte Carlo; Markov random fields; model determination