Exchangeability and sets of desirable gambles

Details Exchangeability and sets of desirable gambles Exchangeability and sets of desirable gambles

2009-11-24

arxiv.org/abs/0911.4727v3

Mathematics

Probability

40 pages

Scientific paper

10.1016/j.ijar.2010.12.002

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.

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