Comparing methods for joint objective and subjective uncertainty propagation with an example in a risk assessment

Probability-boxes, numerical possibility theory and belief functions have been suggested as useful tools to represent imprecise, vague or incomplete information. They are particularly appropriate in environmental risk assessment where information is typically tainted with imprecision or incompleteness. Based on these notions, we present and compare four different methods to propagate objective and subjective uncertainties through multivariate functions. Lastly, we use these different techniques on an environmental real case of soil contamination by lead on an ironworks brownfield.