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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)
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)
Dilation occurs when upper and lower probability estimates of some event E are properly included in the upper and lower probability estimates of the probability of E conditional on another event F, resulting in a change from a more precise estimate of E to a less precise estimate of E upon learning F. Strict dilation occurs when E is dilated by every event(More)
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