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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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Chicago
De Cooman, Gert, and Erik Quaeghebeur. 2010. “Infinite Exchangeability for Sets of Desirable Gambles.” In Communications in Computer and Information Science, ed. Eyke Hüllermeier, Rudolf Kruse, and Frank Hoffmann, 80:60–69. Berlin, Germany: Springer.
APA
De Cooman, Gert, & Quaeghebeur, E. (2010). Infinite exchangeability for sets of desirable gambles. In Eyke Hüllermeier, R. Kruse, & F. Hoffmann (Eds.), Communications in Computer and Information Science (Vol. 80, pp. 60–69). Presented at the 13th International conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2010), 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.
MLA
De Cooman, Gert, and Erik Quaeghebeur. “Infinite Exchangeability for Sets of Desirable Gambles.” Communications in Computer and Information Science. Ed. Eyke Hüllermeier, Rudolf Kruse, & Frank Hoffmann. Vol. 80. Berlin, Germany: Springer, 2010. 60–69. Print.
@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       = {H{\"u}llermeier, Eyke and Kruse, Rudolf and Hoffmann, Frank},
  isbn         = {9783642140549},
  issn         = {1865-0929},
  keyword      = {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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