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.

翻译：高斯图模型能够捕捉变量间的复杂依赖结构。对于此类模型，贝叶斯推断具有吸引力，因为它提供了融入先验信息并通过后验分布量化不确定性的原则性方法。然而，在共轭G-Wishart先验分布下对精度矩阵进行后验计算时，对于一般非可分解图而言成本较高。为此，我们提出一种名为G-Wishart加权提议算法（WWA）的新型马尔可夫链蒙特卡洛（MCMC）方法。WWA的显著特征包括：延迟接受MCMC、精度矩阵的吉布斯更新，以及图空间上的有信息提议分布，该分布支持易并行计算。与现有方法相比，WWA降低了从G-Wishart分布中进行相对昂贵采样的频率。这带来了更快的MCMC收敛性、改进的MCMC混合效果以及更短的计算时间。在模拟数据和真实数据上的数值研究表明，WWA为后验推断提供的工具，相比竞争的最新MCMC算法更为高效。