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Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to represent some common types of uncertainty. Coherent lower(More)
In this paper we try to clarify the notion of independence for imprecise probabilities. Our main point is that there are several possible definitions of independence which are applicable in different types of situation. With this aim, simple examples are given in order to clarify the meaning of the different concepts of independence and the relationships(More)
This paper investigates Walley's concepts of epistemic irrelevance and epistemic independence for imprecise probability models. We study the mathematical properties of irrelevance and independence, and their relation to the graphoid axioms. Examples are given to show that epistemic irrelevance can violate the symmetry, contraction and intersection axioms,(More)
Possibility measures and conditional possibility measures are given a behavioural interpretation as marginal betting rates against events. Under this interpretation, possibility measures should satisfy two consistency criteria, known asàvoiding sure loss' and`coherence'. We survey the rules that have been proposed for deening conditional possibilities and(More)
This is an introduction to the concepts of lower and upper prevision and the mathematical theory of coherence. Upper and lower previsions are generalisations of upper and lower probabilities. They can model a very wide variety of kinds of uncertainty, partial information and ignorance. The theory of coherent lower previsions is based on a simple behavioural(More)
We solve two fundamental problems of probabilistic reasoning: given a finite set of conditional probability assessments, how to determine whether the assessments are mutually consistent, and how to determine what they imply about the conditional probabilities of new events? These problems were posed in 1854 by George Boole, who gave a partial solution using(More)
The paper discusses the problem of modelling linguistic uncertainty, which is the uncertainty produced by statements in natural language. For example, the vague statement`Mary is young' produces uncertainty about Mary's age. We concentrate on simple aarmative statements of the typèsubject is predicate', where the predicate satisses a special condition(More)
In the problem of parametric statistical inference with a ®nite parameter space, we propose some simple rules for de®ning posterior upper and lower probabilities directly from the observed likelihood function, without using any prior information. The rules satisfy the likelihood principle and a basic consistency principle (`avoiding sure loss'), they(More)