Efficient Gaussian graphical model determination under G-Wishart prior distributions

Abstract

This paper proposes a new algorithm for Bayesian model determination in Gaussian graphical models under G-Wishart prior distributions. We first review recent development in sampling from G-Wishart distributions for given graphs, with a particular interest in the efficiency of the block Gibbs samplers and other competing methods. We generalize the maximum clique block Gibbs samplers to a class of flexible block Gibbs samplers and prove its convergence. This class of block Gibbs samplers substantially outperforms its competitors along a variety of dimensions. We next develop the theory and computational details of a novel Markov chain Monte Carlo sampling scheme for Gaussian graphical model determination. Our method relies on the partial analytic structure of G-Wishart distributions integrated with the exchange algorithm. Unlike existing methods, the new method requires neither proposal tuning nor evaluation of normalizing constants of G-Wishart distributions.