Bayesian Estimation for Gaussian Graphical Models: Structure Learning, Predictability, and Network Comparisons

Abstract

Gaussian graphical models (GGM; “networks”) allow for estimating conditional dependence structures that are encoded by partial correlations. This is accomplished by identifying non-zero relations in the inverse of the covariance matrix. In psychology the default estimation method uses ${\mathcal{\ell }}_1$-regularization, where the accompanying inferences are restricted to frequentist objectives. Bayesian methods remain relatively uncommon in practice and methodological literatures. To date, they have not yet been used for estimation and inference in the psychological network literature. In this work, I introduce Bayesian methodology that is specifically designed for the most common psychological applications. The graphical structure is determined with posterior probabilities that can be used to assess conditional dependent and independent relations. Additional methods are provided for extending inference to specific aspects within- and between-networks, including partial correlation differences and Bayesian methodology to quantify network predictability. I first demonstrate that the decision rule based on posterior probabilities can be calibrated to the desired level of specificity. The proposed techniques are then demonstrated in several illustrative examples. The methods have been implemented in the R package BGGM.

Keywords:

• Gaussian graphical model
• Bayesian
• partial correlation
• prediction
• explanation
• Bayesian R2
• networks