scholarly journals Bayesian Structure Learning in Sparse Gaussian Graphical Models

2015 ◽  
Vol 10 (1) ◽  
pp. 109-138 ◽  
Author(s):  
A. Mohammadi ◽  
E. C. Wit
Keyword(s):  
Graphical Models ◽  
Structure Learning ◽  
Gaussian Graphical Models

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

2018 ◽  
Author(s):  
Donald Ray Williams
Keyword(s):  
Graphical Models ◽  
Structure Learning ◽  
Estimation Method ◽  
R Package ◽  
Posterior Probabilities ◽  
Gaussian Graphical Models ◽  
Bayesian Methodology ◽  
Partial Correlations ◽  
Network Comparisons ◽  
Graphical Structure

Gaussian graphical models (GGM; ``networks'') allow for estimating conditional independence 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 $\ell_1$-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, which allow for assessing 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.

scholarly journals Fast Bayesian inference in large Gaussian graphical models

Biometrics ◽  
2019 ◽  
Vol 75 (4) ◽  
pp. 1288-1298
Author(s):  
Gwenaël G. R. Leday ◽  
Sylvia Richardson
Keyword(s):  
Bayesian Inference ◽  
Graphical Models ◽  
Gaussian Graphical Models
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