Introduction to Imprecise Probabilities

Chapter 5Other uncertainty theories based on capacities

Sébastien Destercke¹ and Didier Dubois²

¹National Center for Scientific Research (CNRS), Heuristic and Diagnostic Methods for Complex Systems Laboratory (HeuDiaSyC), University of Technology, Compiègne, France

²National Center for Scientific Research (CNRS), Toulouse Research Institute on Computer Science (IRIT), Paul-Sabatier University, Toulouse, France

Some of the simple mathematical models reviewed in Chapter 4 first emerged as basic building blocks of other uncertainty theories, and not as special instances of coherent lower previsions. In the following, the term uncertainty theories refers to several mathematical models and approaches devoted to the numerical or ordinal representation of beliefs induced by uncertainty due to the variability of phenomena, or the presence of incomplete information, or both. As these theories emerged from different areas and motivations, they led to different requirements, settings or axioms and to different tools for information processing. More precisely, we can enumerate several lines of thought motivating the development of uncertainty theories:

• The idea that in Bayesian approaches to statistics, prior probabilities on model parameters are hard to precisely specify, partly because there is no truly satisfying ‘non-informative’ prior, and partly because probabilities elicited from experts are most of the time imprecise. This is the robust Bayesian approach [64].
• A questioning of ...