Bayesian inference for general Gaussian graphical models with application to multivariate lattice data

TL;DR

This paper develops efficient Bayesian Markov chain Monte Carlo methods for inference in multivariate Gaussian graphical models, including novel autoregressive models for spatial lattice data, demonstrated through simulations and real-world cancer mortality analysis.

Contribution

It introduces new MCMC algorithms for Gaussian graphical models with G-Wishart priors and extends them to flexible spatial autoregressive models for lattice data.

Findings

Effective inference in complex Gaussian graphical models.

Flexible modeling of spatial and outcome correlations.

Successful application to cancer mortality data.

Abstract

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using simulated and real-world examples, including an application to cancer mortality surveillance.