260 research outputs found
Accept & Reject Statement-Based Uncertainty Models
We develop a framework for modelling and reasoning with uncertainty based on
accept and reject statements about gambles. It generalises the frameworks found
in the literature based on statements of acceptability, desirability, or
favourability and clarifies their relative position. Next to the
statement-based formulation, we also provide a translation in terms of
preference relations, discuss---as a bridge to existing frameworks---a number
of simplified variants, and show the relationship with prevision-based
uncertainty models. We furthermore provide an application to modelling symmetry
judgements.Comment: 35 pages, 17 figure
Reasoning with imprecise probabilities
This special issue of the International Journal of Approximate Reasoning (IJAR) grew
out of the 4th International Symposium on Imprecise Probabilities and Their Applications
(ISIPTA’05), held in Pittsburgh, USA, in July 2005 (http://www.sipta.org/isipta05).
The symposium was organized by Teddy Seidenfeld, Robert Nau, and Fabio
G. Cozman, and brought together researchers from various branches interested in imprecision
in probabilities. Research in artificial intelligence, economics, engineering, psychology,
philosophy, statistics, and other fields was presented at the meeting, in a lively
atmosphere that fostered communication and debate. Invited talks by Isaac Levi and
Arthur Dempster enlightened the attendants, while tutorials by Gert de Cooman, Paolo
Vicig, and Kurt Weichselberger introduced basic (and advanced) concepts; finally, the
symposium ended with a workshop on financial risk assessment, organized by Teddy
Seidenfeld
Constructing imprecise probabilities using arguments as evidence
This paper addresses the problem of constructing subjective imprecise probabilities using qualitative and conflicting pieces of information (arguments) as evidence.We propose formulae for the calculus of imprecise probabilities and show that the probabilities obtained reflect the indeterminacy of the subject, faithfully quantify the support offered by the arguments and constitute previsions that are mathematically coherent in the sense of [Walley, 1991]
Exchangeability and sets of desirable gambles
Sets of desirable gambles constitute a quite general type of uncertainty
model with an interesting geometrical interpretation. We give a general
discussion of such models and their rationality criteria. We study
exchangeability assessments for them, and prove counterparts of de Finetti's
finite and infinite representation theorems. We show that the finite
representation in terms of count vectors has a very nice geometrical
interpretation, and that the representation in terms of frequency vectors is
tied up with multivariate Bernstein (basis) polynomials. We also lay bare the
relationships between the representations of updated exchangeable models, and
discuss conservative inference (natural extension) under exchangeability and
the extension of exchangeable sequences.Comment: 40 page
Argumentation as a practical foundation for decision theory
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