Introduction to Imprecise Probabilities

Chapter 3Structural judgements

Enrique Miranda¹ and Gert de Cooman²

¹Department of Statistics and Operations Research, University of Oviedo, Spain

²SYSTeMS Research Group, Ghent University, Belgium

3.1 Introduction

In Chapters 1 and 2, we have come across a number of local probability assessments: stating that certain gambles are desirable, or providing lower and upper previsions for given gambles. We have learnt how to make inferences based on such local assessments, by deriving the least committal coherent models that are compatible with them—meaning that they include them (for sets of desirable gambles) or dominate them (for lower previsions). The present chapter deals with structural judgements: assessments that a subject makes about global properties of her belief model. They include assessments of independence and symmetry, and they are important when dealing with imprecise probability models, where they have to be combined with local assessments to find the least committal models that are compatible with these local assessments and still satisfy the global properties.

As we know from previous chapters, imprecise probability assessments can take many different forms: coherent lower previsions, sets of desirable gambles or sets of linear previsions. In this chapter, we will briefly describe how two specific types of structural judgements—independence and symmetry—can be incorporated into these formulations.

Section 3.2 deals with irrelevance and independence. When working ...