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

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.