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Bayesian Uncertainty Estimation for Gaussian Graphical Models and Centrality Indices
Joran Jongerling1, Sacha Epskamp2,3, Donald R Williams4
1Department of Methodology and Statistics, Tilburg School of Social and Behavioral Sciences, Tilburg University.
Multivariate Behavioral Research
|February 18, 2022
Summary
Bayesian graphical LASSO (GLASSO) network estimation improves accuracy for psychopathology symptom networks compared to frequentist methods. This approach better estimates symptom influences and centrality measures, offering a more reliable network analysis.
Area of Science:
- Psychology
- Network Science
- Computational Statistics
Background:
- The network approach to psychopathology views psychological disorders as systems of interacting components, such as symptoms.
- Centrality indices are used to quantify symptom influence within these networks, but estimation methods like frequentist graphical LASSO (GLASSO) face challenges with bias and uncertainty.
- Bayesian estimation methods offer potential advantages in handling sampling distribution biases of centrality indices.
Purpose of the Study:
- To compare the performance of Bayesian GLASSO with Horseshoe priors against frequentist GLASSO for estimating psychopathology symptom networks.
- To evaluate the accuracy and reliability of centrality measures derived from different estimation methods.
Main Methods:
- Extensive simulations were conducted to compare Bayesian GLASSO (using GLASSO and Horseshoe priors) with frequentist GLASSO.
- The study assessed bias in edge weights, centrality measures, correlation between estimated and true partial correlations, specificity, and sensitivity.
- Coverage of uncertainty in centrality measures (strength, closeness, betweenness) was also evaluated.
Main Results:
- Bayesian GLASSO demonstrated superior performance over the Horseshoe prior and outperformed frequentist GLASSO in reducing bias for edge weights and centrality measures.
- The Bayesian GLASSO showed better correlation between estimated and true partial correlations and improved specificity.
- While sensitivity was slightly better for frequentist GLASSO, Bayesian GLASSO achieved good coverage for strength and closeness centrality, though less so for betweenness centrality.
Conclusions:
- Bayesian GLASSO provides a more accurate and less biased method for estimating psychopathology symptom networks compared to frequentist GLASSO.
- This Bayesian approach offers improved estimation of symptom influences and key centrality indices, enhancing the reliability of network analyses in psychopathology.
- Further research may be needed to refine the estimation of betweenness centrality uncertainty within Bayesian network models.
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