Modeling uncertainty with belief functions in numerical models

Abstract

In this paper a new approach for the representation and the analysis of uncertain, incomplete, partial information in numerical models is introduced and discussed. It is based on Shafer's mathematical theory of evidence. This theory allows a more flexible and realistic description and formalization of the available information than the usual probabilistic models. For example it renders possible the combination of evidence coming from different sources, opinions of experts, etc. It also allows for contradicting evidence. It permits one to better incorporate subjective judgements either concerning input variables or relations between different variables. This is done using Shafer's belief functions which can be seen as random sets, in particular random intervals. The method is a generalization of well known risk analysis techniques. The evaluation of large models requires Monte Carlo sampling generalized to intervals which can be treated according to interval arithmetics.