Uncertainties in conditional probability tables of discrete Bayesian Belief Networks: A comprehensive review. (February 2020) - Rohmer, Jeremy
Abstract: Discrete Bayesian Belief Network (BBN) has become a popular method for the analysis of complex systems in various domains of application. One of its pillar is the specification of the parameters of the probabilistic dependence model (i.e. the cause–effect relation) represented via a Conditional Probability Table (CPT). Depending on the available data (observations, prior knowledge, expert-based information, etc.), CPTs can be populated in different manners, i.e. different assumptions can be made and different methods are available, which might lead to uncertain BBN-based results. Through an extensive review study of the past ten years, we aim at addressing three questions related to the CPT uncertainties. First, we show how to constrain these uncertainties either using elicitation of expert inputs, or using a combination of scarce data and expert-derived information. Second, we show how to integrate these uncertainties in the BBN-based analysis through propagation procedures either using probabilities or imprecise probabilities within the setting of credal or evidential networks. Finally, we show how to test the robustness of the BBN-based results to these uncertainties via sensitivity analysis specifically dedicated to BBNs. A special care was paid to describe the best practices for the implementation of the reviewed methods and the remaining gaps. Highlights: Extensive review survey on the question of uncertainties of CPTs of discrete BBNs. First question addresses how to constrain these uncertainties. Second question addresses how to propagate them. Third question addresses how to test the robustness to them. Absence of extensive benchmark exercise covering all three questions is underlined.