Comment on Vogels et al.'s (2024)"Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison": An updated performance check using BGGM

2026-09-25

AI Summary

This study addresses a methodological bias in the evaluation by Vogels et al., where inconsistent prior graph density settings led to an unfair assessment of BGGM’s performance in Gaussian graphical model structure learning. To rectify this, we conduct comparative experiments using the R package BGGM and Monte Carlo simulations, unifying prior probability parameters across methods to ensure a fair evaluation. Our work reveals the critical impact of prior specification on Bayesian method comparisons and corrects conclusions drawn in the original literature. The results demonstrate that, after calibrating the priors, BGGM achieves performance comparable to other Bayesian approaches. This research provides a more rigorous methodological reference for model evaluation in related fields, emphasizing the necessity of consistent prior settings when benchmarking Bayesian structure learning algorithms.

Abstract

Vogels et al. (2024) presented an empirical comparison of Bayesian methods for structure learning in undirected Gaussian graphical models. The method implemented in the R package BGGM was run with equal prior probabilities for a null, negative, and positive partial correlation, implying a prior inclusion probability (equivalent to a prior graph density) of 2/3. The other Bayesian methods in the comparison used a prior graph density of 0.2 however. The data-generating densities ranged from 0.01 to 0.1. This resulted in a substantial overestimation of the inclusion probabilities of absent edges by BGGM. For a fair comparison of the performance of the different methods, I repeated the simulation using a prior inclusion probability of 0.2 using BGGM. In this case, the performance of BGGM is comparable with the other Bayesian methods.

Problem

• Bayesian structure learning
• Gaussian graphical models
• prior graph density
• empirical comparison
• BGGM

Innovation

• Bayesian structure learning
• Gaussian graphical models
• prior inclusion probability
• BGGM
• empirical comparison