#### Filter Results:

#### Publication Year

1996

2011

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

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)

1.1 INTRODUCTION Information is commonly transmitted through statements in natural language. The statement 'Mary is young', for instance, provides partial information about Mary's age. If initially we know nothing about Mary's age and we subsequently hear that she is young, our knowledge about her age has increased, although we remain uncertain about her… (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)

- Gregory Wheeler, Isaac Levi, Peter Walley, Teddy Seidenfeld, James Joyce, Fabio Cozman
- 2011

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)

- ‹
- 1
- ›