Robust Bayesian structure learning for graphical models with T-distributions using G-Wishart prior

Accurately interpreting complex relationships among many variables is of significant importance in science. One appealing approach to this task is Bayesian Gaussian graphical modeling, which has recently undergone numerous improvements. However, this model may struggle with datasets containing outliers; replacing Gaussian distributions with t-distributions enhances inferences and handles datasets with outliers. In this paper, we aim to address the challenges of Gaussian graphical models through t-distributions graphical models. To this end, we draw inspiration from the Birth–Death Monte Carlo Markov Chain (BDMCMC) algorithm and introduce a Bayesian method for structure learning in both classical and alternative t-distributions graphical models. We also demonstrate that the more flexible model outperforms the other when applied to more complex generated data. This is illustrated using a wide range of simulated datasets as well as a real-world dataset.