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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)

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)

- Isobel AP Parkin, Chushin Koh, Haibao Tang, Stephen J Robinson, Sateesh Kagale, Wayne E Clarke +26 others
- Genome Biology
- 2014

Brassica oleracea is a valuable vegetable species that has contributed to human health and nutrition for hundreds of years and comprises multiple distinct cultivar groups with diverse morphological and phytochemical attributes. In addition to this phenotypic wealth, B. oleracea offers unique insights into polyploid evolution, as it results from multiple… (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)

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)

- Peter Walley, Serafõ Ân Moral
- 1997

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)

- Peter Walley
- 1998

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)

· Diets rich in broccoli (Brassica oleracea var italica) have been associated with maintenance of cardiovascular health and reduction in risk of cancer. These health benefits have been attributed to glucoraphanin that specifically accumulates in broccoli. The development of broccoli with enhanced concentrations of glucoraphanin may deliver greater health… (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)