A new approach to updating beliefs
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
Epistemic irrelevance on sets of desirable gambles
Annals of Mathematics and Artificial Intelligence
Notes on “Notes on conditional previsions”
International Journal of Approximate Reasoning
Notes on conditional previsions
International Journal of Approximate Reasoning
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
Sequential decision making with partially ordered preferences
Artificial Intelligence
Exchangeability and sets of desirable gambles
International Journal of Approximate Reasoning
Conglomerable natural extension
International Journal of Approximate Reasoning
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
Artificial Intelligence
International Journal of Approximate Reasoning
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We detail the relationship between sets of desirable gambles and conditional lower previsions. The former is one the most general models of uncertainty. The latter corresponds to Walley's celebrated theory of imprecise probability. We consider two avenues: when a collection of conditional lower previsions is derived from a set of desirable gambles, and its converse. In either case, we relate the properties of the derived model with those of the originating one. Our results constitute basic tools to move from one formalism to the other, and thus to take advantage of work done in the two fronts.