Bayesian Graphical Lasso Models and Efficient Posterior Computation

Abstract

Recently, the graphical lasso procedure has become popular in estimating Gaussian graphical models. In this paper, we introduce a fully Bayesian treatment of graphical lasso models. We first investigate the graphical lasso prior that has been relatively unexplored. Using data augmentation, we develop a simple but highly efficient block Gibbs sampler for simulating covariance matrices. We then generalize the Bayesian graphical lasso to the Bayesian adaptive graphical lasso. Finally, we illustrate and compare the results from our approach to those obtained using the standard graphical lasso procedures for real and simulated data. In terms of both covariance matrix estimation and graphical structure learning, the Bayesian adaptive graphical lasso appears to be the top overall performer among a range of frequentist and Bayesian methods.