Introduction to Imprecise Probabilities

Chapter 4Special cases

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

4.1 Introduction

As argued in Chapters 1 and 2, lower previsions and sets of desirable gambles are very general models of uncertainty that have solid foundations and a clear behavioural interpretation. However, this generality goes along with a high computational complexity and a difficulty to easily explain such representations to users that are not experts in imprecise probability theories.

Therefore, in practical applications, simplified representations can greatly improve the applicability of imprecise probability theories. There are three main reasons for using simplified representations:

• to facilitate the elicitation or information collection process;
• to improve the computational tractability of mathematical models;
• to improve the interpretability of results when answering some particular question of interest.

The main objection to the use of such representations, or more precisely for restricting oneself to them, is that they may not be general enough to exactly model the available information. Moreover, even if some pieces of information can be exactly modelled by such simplified representations, ...