The use of sets of stochastic operators to constructing imprecise probabilities

Abstract

A new approach to constructing sets of probabilities is presented. We use sets of stochastic operators that represent rules that preserve desirability of gambles. We also provide a set of criteria that allow constructing imprecise probability models consistent with the desirability preserving rules. The model is more general than the standard imprecise probability models using lower and upper previsions. The greater generality means that credal sets and therefore lower previsions can be understood as a special case. Some results on extensions of such models are also provided that generalise the corresponding results from the theory of lower and upper previsions. © 2010 Springer-Verlag Berlin Heidelberg.