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Infinite exchangeability for sets of desirable gambles

Gert De Cooman (UGent) and Erik Quaeghebeur (UGent)
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Abstract
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study infinite exchangeability assessments for them, and give a counterpart of de Finetti's infinite representation theorem. We show how the infinite 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.
Keywords
sets of desirable gambles, weak desirability, natural extension, coherence, desirability, exchangeability, representation, updating

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MLA
De Cooman, Gert, and Erik Quaeghebeur. “Infinite Exchangeability for Sets of Desirable Gambles.” Communications in Computer and Information Science, edited by Eyke Hüllermeier et al., vol. 80, Springer, 2010, pp. 60–69.
APA
De Cooman, G., & Quaeghebeur, E. (2010). Infinite exchangeability for sets of desirable gambles. In E. Hüllermeier, R. Kruse, & F. Hoffmann (Eds.), Communications in Computer and Information Science (Vol. 80, pp. 60–69). Berlin, Germany: Springer.
Chicago author-date
De Cooman, Gert, and Erik Quaeghebeur. 2010. “Infinite Exchangeability for Sets of Desirable Gambles.” In Communications in Computer and Information Science, edited by Eyke Hüllermeier, Rudolf Kruse, and Frank Hoffmann, 80:60–69. Berlin, Germany: Springer.
Chicago author-date (all authors)
De Cooman, Gert, and Erik Quaeghebeur. 2010. “Infinite Exchangeability for Sets of Desirable Gambles.” In Communications in Computer and Information Science, ed by. Eyke Hüllermeier, Rudolf Kruse, and Frank Hoffmann, 80:60–69. Berlin, Germany: Springer.
Vancouver
1.
De Cooman G, Quaeghebeur E. Infinite exchangeability for sets of desirable gambles. In: Hüllermeier E, Kruse R, Hoffmann F, editors. Communications in Computer and Information Science. Berlin, Germany: Springer; 2010. p. 60–9.
IEEE
[1]
G. De Cooman and E. Quaeghebeur, “Infinite exchangeability for sets of desirable gambles,” in Communications in Computer and Information Science, Dortmund, Germany, 2010, vol. 80, pp. 60–69.
@inproceedings{984155,
  abstract     = {Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study infinite exchangeability assessments for them, and give a counterpart of de Finetti's infinite representation theorem. We show how the infinite 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.},
  author       = {De Cooman, Gert and Quaeghebeur, Erik},
  booktitle    = {Communications in Computer and Information Science},
  editor       = {Hüllermeier, Eyke and Kruse, Rudolf and Hoffmann, Frank},
  isbn         = {9783642140549},
  issn         = {1865-0929},
  keywords     = {sets of desirable gambles,weak desirability,natural extension,coherence,desirability,exchangeability,representation,updating},
  language     = {eng},
  location     = {Dortmund, Germany},
  pages        = {60--69},
  publisher    = {Springer},
  title        = {Infinite exchangeability for sets of desirable gambles},
  url          = {http://dx.doi.org/10.1007/978-3-642-14055-6_7},
  volume       = {80},
  year         = {2010},
}

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