Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model

We consider a model for the risk-based design of a flood protection dike, and use probability distributions to represent aleatory uncertainty and possibility distributions to describe the epistemic uncertainty associated to the poorly known parameters of such probability distributions. A hybrid method is introduced to hierarchically propagate the two types of uncertainty, and the results are compared with those of a Monte Carlo-based Dempster-Shafer approach employing independent random sets and a purely probabilistic, two-level Monte Carlo approach: the risk estimates produced are similar to those of the Dempster-Shafer method and more conservative than those of the two-level Monte Carlo approach.