Sensitivity analysis of prior beliefs in advanced Bayesian networks

Bayesian Network (BN) is an efficient model tool for approximate reasoning based on machine learning. It has been widely used for supporting the decision in many engineering applications such as geotechnical engineering. However, the current studies on BN are mostly on uncertainty quantification and decision-making, while the sensitivity analysis on BN, which may provide much more insights for decision-making, has not received much attention. The current research on sensitivity analysis of BN mainly focuses on local method, and there is a need to develop global sensitivity analysis (GSA) for both forward and backward inferences of BN. We present in this paper GSA analysis for BN within two different settings. For the first setting, it is assumed that the BN nodes, as well as their connection are characterized by precise (conditional) probabilities, and we introduce GSA for both forward and backward analysis. It is shown that, by forward analysis, the GSA indices can effectively identify the nodes which make the most contribution to the end nodes directly related to the reliability; by backward analysis, the GSA indices can inform the most important information needs to be collected for BN model updating. The second setting concerns the incomplete knowledge of nodes and their connections, and it is assumed these quantities are characterized by imprecise probability models. In this setting, the GSA is then introduced, and implemented with the newly developed non-intrusive imprecise stochastic simulation (NISS) method, for learning the most important epistemic uncertainty sources, by reducing which the robustness of the BN inference can be enhanced the most. The above theoretical developments are then applied to an infinite slope reliability analysis problem.