13. Advancing multilevel Bayesian network with efficient Bayesian inference

Bayesian networks (BN) provide a powerful framework for modeling complex dependencies and reasoning, under uncertainty across diverse applications. A multilevel Bayesian network (MBN) combines BNs with multilevel modeling, facilitating their applications in datasets involving correlated observations. However, the robustness of multilevel models is highly affected by the number of clusters and cluster size. Thus, the reproducibility of MBN is questionable in small sample scenarios. Bayesian methods facilitate the integration of prior knowledge, thereby robustifying inference for small samples sizes. Bayesian inference is often performed using Markov Chain Monte Carlo methods which is known to be computationally intensive. Therefore, this study aims to use the integrated nested Laplace approximation (INLA) to efficiently compute the local network scores during structure learning, and subsequent parameter learning. In addition, the study investigates the prior sensitivity in structure and parameter learning of MBN and compares the results with MBN based on the maximum likelihood estimation (MLE) technique. The study uses simulation study considering data with different numbers of clusters (20, 30, 50), with five individuals per cluster in each scenario. For each scenario, we considered the usual log-Gamma and Penalized Complexity (PC) priors on the precision parameters in the single random effect case, and Wishart and LKJ priors for cases with more than one random effects. Results show that the structure and parameters of MBN are sensitive under different prior settings and the performance of MBN with a log-gamma prior on the precision parameter of each local network is higher as compared to MBN fitted with MLE.

Correlated observations

Integrated nested Laplace approximation

Multilevel Bayesian network

Maximum likelihood estimation

Log-Gamma prior

Penalizing complexity prior 

Mid-Level

Knowledge

Women in Statistics and Data Science 2025