Prior Sensitivity in Multilevel Bayesian Networks with a Single Random Effect Using Efficient Bayesian Inference; Small Sample Scenario.

Bezalem Eshetu Yirdaw (Ph.D. Candidate), MSc in Statistics, University of South Africa.

Abstract

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 four different numbers of clusters (10, 20, 30, 50), with five individuals per cluster in each scenario. The usual log-Gamma and Penalizing Complexity priors on the precision parameters, as well as user-defined priors on the regression coefficients of each local network under different settings were considered, for each scenario. 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.

About the Presenter

Bezalem Eshetu Yirdaw is a final year PhD candidate in the Department of Statistics at the University of South Africa. Her doctoral research focuses on Bayesian network models for analyzing correlated data including multilevel and longitudinal data. Before starting her PhD, she worked as a lecturer at various universities in Ethiopia. She is a recipient of the L’Oréal-UNESCO For Women in Science Sub-Saharan Africa Award and a Schlumberger Foundation Faculty for the Future Fellow. Bezalem has published several papers from her PhD in peer-reviewed journals, with more under review. She has also received travel awards to present her work at the 16th Bayesian Network Modeling Association (BNMA) Conference and the 19th SUSAN-IBS Conference.