Bayesian structural learning and estimation in Gaussian graphical models

We propose a new stochastic search algorithm for Gaussian graphical models called the mode oriented stochastic search. Our algorithm relies on the existence of a method to accurately and efficiently approximate the marginal likelihood associated with a graphical model when it cannot be computed in closed form. To this end, we develop a new Laplace approximation method to the normalizing constant of a G-Wishart distribution. We show that combining the mode oriented stochastic search with our marginal likelihood estimation method leads to excellent results with respect to other techniques discussed in the literature. We also describe how to perform inference through Bayesian model averaging based on the reduced set of graphical models identified. Finally, we give a novel stochastic search technique for multivariate regression models. Some key words: Bayesian model averaging; Covariance estimation; Covariance selection; Gaussian graphical models; Multivariate regression; Stochastic search.