  Bayesian graphical models are a useful tool for understanding dependence
relationships among many variables, particularly in situations with external
prior information. In high-dimensional settings, the space of possible graphs
becomes enormous, rendering even state-of-the-art Bayesian stochastic search
computationally infeasible. We propose a deterministic alternative to estimate
Gaussian and Gaussian copula graphical models using an Expectation Conditional
Maximization (ECM) algorithm, extending the EM approach from Bayesian variable
selection to graphical model estimation. We show that the ECM approach enables
fast posterior exploration under a sequence of mixture priors, and can
incorporate multiple sources of information.
