Abstract

We propose a methodology for Bayesian model determination in decomposable graphical gaussian models. To achieve this aim we consider a hyper inverse Wishart prior distribution on the concentration matrix for each given graph. To ensure compatibility across models, such prior distributions are obtained by marginalisation from the prior conditional on the complete graph. We explore alternative structures for the hyperparameters of the latter, and their consequences for the model. Model determination is carried out by implementing a reversible jump MCMC sampler. In particular, the dimension-changing move we propose involves adding or dropping an edge from the graph. We characterise the set of moves which preserve the decomposability of the graph, giving a fast algorithm for maintaining the junction tree representation of the graph at each sweep. As state variable, we propose to use the incomplete variance-covariance matrix, containing only the elements for which the correspondi...

Citations