Abstract

Co-authors: Jack Jewson and David Rossell. Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, that is on the plausibility of conditional independence statements given the data, and on parameter estimates. However, computational demands have limited their application when the number of variables is large, which prompted the use of pseudo-Bayesian approaches. We propose fully Bayesian algorithms that provably scale well to high dimensions when the data-generating precision matrix is sparse, at a similar cost to the best available pseudo-Bayesian methods. Our examples show that the methods extend the applicability of exact Bayesian inference from roughly one hundred to roughly one thousand variables (equivalently, from 5,000 edges to 500,000 edges) if one desires a solution within a few seconds or minutes. All methods are implemented in the R package mombf.