The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks

Their use as a decision support tool in business and OR has been increasing over the years, including case studies in project management (van Dorp, 2020), supply chain (Garvey et al., 2015), marketing (Hosseini, 2021), and logistics (Qazi, 2022), among others. BNs are defined by two components: a directed acyclic graph (DAG) where each node is a variable of interest and edges represent the, possibly causal, relationship between them; a conditional probability table (CPT) for each node of the DAG reporting the probability distribution of the associated variable conditional on its parents. BNs are highly interpretable due to their graphical nature, representing the probabilistic relationships between variables, making it easy for users to understand and trace the influence of one variable on another. With explainability now recognized as critical for the use of AI in applied research (Rudin, 2019), including in OR (De Bock et al., 2023), BNs stand out by providing transparent and intuitive explanations, thereby enhancing trust and clarity in decision-making processes. The underlying DAG and the associated CPTs can be learned from data using machine learning algorithms or elicited using experts' opinions and knowledge. There is now a vast amount of algorithms to learn BN from data (e.g.