Bayesian update of the parameters of probability distributions for risk assessment in a two-level hybrid probabilistic-possibilistic uncertainty framework

Risk analysis models describing aleatory (i.e., random) events contain parameters (e. g., probabilities, failure rates, ...) that are epistemically uncertain, i.e., known with poor precision. Whereas probability distributions are always used to describe aleatory uncertainty, alternative frameworks of representation may be considered for describing epistemic uncertainty, depending on the information and data available. In this paper, we use possibility distributions to describe the epistemic uncertainty in the parameters of the (aleatory) probability distributions. We address the issue of updating, in a Bayesian framework, the possibilistic representation of the epistemically-uncertain parameters of (aleatory) probability distributions as new information (e. g., data) becomes available. A purely possibilistic counterpart of the classical, well-grounded probabilistic Bayes theorem is adopted. The feasibility of the method is shown on a literature case study involving the risk-based design of a flood protection dike.