Generic reversible jump MCMC using graphical models

Markov chain Monte Carlo techniques have revolutionized the field of Bayesian statistics. 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 (TD) models is not easy and available software may lack the flexibility required for dealing with the complexities of real data, often because it does not allow the TD model to be simply part of some bigger model. In this paper we describe a class of widely applicable TD models that can be represented by a generic graphical model, which may be incorporated into arbitrary other graphical structures without significantly affecting the mechanism of inference. We also present a decomposition of the reversible jump algorithm into abstract and problem-specific components, which provides infrastructure for applying the method to all models in the class considered. These developments represent a first step towards a context-free method for implementing TD models that will facilitate their use by applied scientists for the practical exploration of model uncertainty. Our approach makes use of the popular WinBUGS framework as a sampling engine and we illustrate its use via two simple examples in which model uncertainty is a key feature.