Arbitrarily high degree elevation of Be´zier representations
Computer Aided Geometric Design
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Belief models: An order-theoretic investigation
Annals of Mathematics and Artificial Intelligence
Epistemic irrelevance on sets of desirable gambles
Annals of Mathematics and Artificial Intelligence
Notes on conditional previsions
International Journal of Approximate Reasoning
Sets of desirable gambles: Conditioning, representation, and precise probabilities
International Journal of Approximate Reasoning
Notes on desirability and conditional lower previsions
Annals of Mathematics and Artificial Intelligence
Conglomerable natural extension
International Journal of Approximate Reasoning
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
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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.