Exploring causal reasoning for explainable resilience quantification

While the concept of resilience inspired overall risk quantification, analysis and management, causal modeling and inference based mainly on directed labeled acyclic graphs (DAGs) changed the application of advanced statistical methods to a wide range of human and societal, engineering and natural sciences. The question is formulated how to relate both advanced approaches to draw mutual advantage of each other. This is conducted by extending direct causal chain-like linking of threat events to damage events by considering all possible causal relations. The focus is to motivate this generalization by resorting to the application of the total law of probability, the chain rule, commutation of events conditioned upon, as well as by introducing a binary operator to consider or not the additional dependencies introduced. Thus, for resilience quantification probabilities using random elements representing seed, intermediate and damage events are provided as joint probability function expansions using conditional probability factors that can be visualized with DAGs. This allows to apply weighted graph models to visualize as well as to compute overall risks, including under simplifying assumptions. Examples illustrate expressions with up to two intermediate event transition layers The approach is discussed and how it enables future interfacing between resilience engineering quantification and causal approaches, as well as the option of a recursive generation of a causality inspired resilience quantification expression.

Keywords: Causal modeling and inference, Resilience expansion and quantification, Chain rule and inclusionexclusion principle of probability, Probabilistic graphical model, Risk based on probabilities of random variable measuring consequences, labeled directed acyclic graph.