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Bayesian methods for learning Gaussian graphical models offer a robustframework that addresses model uncertainty and incorporates prior knowledge.Despite their theoretical strengths, the applicability of Bayesian methods isoften constrained by computational needs, especially in modern contextsinvolving thousands of variables. To overcome this issue, we introduce twonovel Markov chain Monte Carlo (MCMC) search algorithms that have asignificantly lower computational cost than leading Bayesian approaches. Ourproposed MCMC-based search algorithms use the marginal pseudo-likelihoodapproach to bypass the complexities of computing intractable normalizingconstants and iterative precision matrix sampling. These algorithms can deliverreliable results in mere minutes on standard computers, even for large-scaleproblems with one thousand variables. Furthermore, our proposed method iscapable of addressing model uncertainty by efficiently exploring the fullposterior graph space. Our simulation study indicates that the proposedalgorithms, particularly for large-scale sparse graphs, outperform the leadingBayesian approaches in terms of computational efficiency and precision. Theimplementation supporting the new approach is available through the R packageBDgraph.

Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood