Representing parametric probabilistic models tainted with imprecision

Numerical possibility theory, belief functions have been suggested as useful tools to represent imprecise, vague or incomplete information. They are particularly appropriate in uncertainty analysis where information is typically tainted with imprecision or incompleteness. Based on their experience or their knowledge about a random phenomenon, experts can sometimes provide a class of distributions without being able to precisely specify the parameters of a probability model. Frequentists use two-dimensional Monte-Carlo simulation to account for imprecision associated with the parameters of probability models. They hence hope to discover how variability and imprecision interact. This paper presents the limitations and disadvantages of this approach and propose a fuzzy random variable approach to treat this kind of knowledge.