Block Structured Graph Priors in Gaussian Graphical Models

Abstract

AbstractGaussian graphical models are a powerful statistical tool to describe the concept of conditional independence between variables through a map between a graph and the family of multivariate normal models. The structure of the graph is unknown and has to be learned from the data. Inference is carried out in a Bayesian framework: thus, the structure of the precision matrix is constrained by the graph through a \({\text {G-Wishart}}\) prior distribution. In this work we first introduce a prior distribution to impose a block structure in the adjacency matrix of the graph. Then we develop a Double Reversible Jump Monte Carlo Markov chain that avoids any \({\text {G-Wishart}}\) normalizing constant calculation when comparing graphical models. The novelty of this procedure is that it looks for block structured graphs, hence proposing moves that add or remove not just a single link but an entire group of them.KeywordsBayesian statisticsDouble reversible jumpG-Wishart prior