Fast Bayesian inference in large Gaussian graphical models.

Area of Science:

• Statistics
• Computational Biology
• Machine Learning

Background:

• Bayesian inference in high-dimensional Gaussian graphical models is computationally intensive due to large model spaces.
• Existing methods struggle with scalability for modern, large-scale datasets.

Purpose of the Study:

• To develop a computationally efficient method for inferring graphical structures in high-dimensional Gaussian models.
• To bypass the exploration of the entire model space for faster inference.

Main Methods:

• Introduced closed-form Bayes factors under the Gaussian conjugate model to test hypotheses of marginal and conditional independence.
• Developed an efficient computation for Bayes factors across all variable pairs.
• Derived exact tail probabilities for Bayes factor null distributions to enable multiplicity correction.

Main Results:

• The proposed method offers extremely efficient computation of Bayes factors for large-scale problems.
• The approach successfully infers marginal and conditional independence structures.
• Demonstrated effectiveness on simulated data and a large gene expression dataset from The Cancer Genome Atlas.

Conclusions:

• The method provides a scalable and efficient solution for Bayesian inference in high-dimensional Gaussian graphical models.
• Enables robust control of error rates for edge inclusion through multiplicity correction.
• Applicable to large biological datasets and other complex systems.