Empirical Comparison of Two Methods for the Bayesian Update of the Parameters of Probability Distributions in a Two-Level Hybrid Probabilistic-Possibilistic Uncertainty Framework for Risk Assessment

In this paper, the authors 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. Two approaches are considered: the first is based on a purely possibilistic counterpart of the classical, well-grounded probabilistic Bayes’ theorem; the second relies on the hybrid combination of (1) fuzzy interval analysis (FIA) to process the uncertainty described by possibility distributions, and (2) repeated Bayesian updating of the uncertainty represented by probability distributions. The feasibility of the two methods is shown on a literature case study involving the risk-based design of a flood protection dike.