Special cases
Sébastien Destercke, Didier Dubois · Wiley series in probability and statistics · 2014
In practical applications, simplified representations can greatly improve the applicability of imprecise probability theories. This chapter reviews several simplified representations that are special cases of coherent lower previsions. For each representation, its interests and limitations are emphasized. The chapter defines and lists the properties of 2-monotone capacities. Probability intervals on singletons are popular representations that play an important role in graphical models and in classification procedures. ∞-monotone capacities also play an important role as special cases of coherent lower probabilities. The chapter discusses some practical representations such as possibility distributions, p-boxes and clouds, which are linked by the fact that they correspond to assessments over some collections of nested sets. Starting from an initial probability measure, neighbourhood models consist in weakening this initial information by means of a discounting parameter. Three main neighbourhood are discussed in the chapter: the pari-mutuel model, the linear-vacuous model and the odds-ratio model.