Mcmc Using Graphical Models

Markov chain Monte Carlo techniques have revolutionized the field of Bayesian statistics. Their enormous power and their generalizability have rendered them the method of choice for statistical inference in many scientific disciplines. Their power is so great that they can even accommodate situations in which the structure of the statistical model itself is uncertain. However, the analysis of such “trans-dimensional” models is not easy, with several significant technical and practical difficulties to overcome. In this paper we present a class of graphical models that allow relatively straightforward analysis of a subset of these trans-dimensional problems. We also present a ‘guided tour’ of the reversible jump methodology underlying our approach and discuss how each of the various difficulties has been circumvented. Our approach has been implemented using the WinBUGS framework as a Gibbs-Metropolis sampling ‘engine’. The main advantage of this is that it affords the analyst much modelling flexibility: trans-dimensional sub-graphs may be used as generic components within an arbitrarily wide range of Bayesian graphical models. We present three example analyses to illustrate our approach.