The G-Wishart Weighted Proposal Algorithm: Efficient Posterior Computation for Gaussian Graphical Models

TL;DR

The paper introduces the G-Wishart weighted proposal algorithm (WWA), an efficient MCMC method for Bayesian inference in Gaussian graphical models that reduces computation time and improves convergence.

Contribution

It presents a novel MCMC algorithm with informed proposals and parallelizable updates, significantly enhancing posterior computation for complex Gaussian graphical models.

Findings

WWA achieves faster convergence than existing methods.

It reduces computational costs by decreasing sampling frequency from the G-Wishart distribution.

Numerical studies demonstrate improved efficiency on simulated and real data.

Abstract

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the posterior distribution. However, posterior computation under the conjugate G-Wishart prior distribution on the precision matrix is expensive for general non-decomposable graphs. We therefore propose a new Markov chain Monte Carlo (MCMC) method named the G-Wishart weighted proposal algorithm (WWA). WWA's distinctive features include delayed acceptance MCMC, Gibbs updates for the precision matrix and an informed proposal distribution on the graph space that enables embarrassingly parallel computations. Compared to existing approaches, WWA reduces the frequency of the relatively expensive sampling from the G-Wishart distribution. This results in faster MCMC convergence, improved MCMC mixing and reduced computing time. Numerical studies on simulated and real data show that WWA provides a more efficient tool for posterior inference than competing state-of-the-art MCMC algorithms.