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Characterizing the set of coherent lower previsions with a finite number of constraints or vertices

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Abstract
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation of this criterion that only uses a finite number of constraints. Any such lower prevision is coherent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results.
Keywords
coherence, lower previsions, polytopes, constraints, vertices, extreme points, characterization, computation

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Chicago
Quaeghebeur, Erik. 2010. “Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or Vertices.” In Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, ed. Peter Grünwald and Peter Spirtes, 466–473. Corvallis, OR, USA: AUAI Press.
APA
Quaeghebeur, E. (2010). Characterizing the set of coherent lower previsions with a finite number of constraints or vertices. In P. Grünwald & P. Spirtes (Eds.), Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (pp. 466–473). Presented at the 26th Conference on Uncertainty in Artificial Intelligence (UAI 2010), Corvallis, OR, USA: AUAI Press.
Vancouver
1.
Quaeghebeur E. Characterizing the set of coherent lower previsions with a finite number of constraints or vertices. In: Grünwald P, Spirtes P, editors. Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence. Corvallis, OR, USA: AUAI Press; 2010. p. 466–73.
MLA
Quaeghebeur, Erik. “Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or Vertices.” Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence. Ed. Peter Grünwald & Peter Spirtes. Corvallis, OR, USA: AUAI Press, 2010. 466–473. Print.
@inproceedings{984156,
  abstract     = {The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation of this criterion that only uses a finite number of constraints. Any such lower prevision is coherent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results.},
  author       = {Quaeghebeur, Erik},
  booktitle    = {Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence},
  editor       = {Gr{\"u}nwald, Peter and Spirtes, Peter},
  isbn         = {9780974903965},
  keyword      = {coherence,lower previsions,polytopes,constraints,vertices,extreme points,characterization,computation},
  language     = {eng},
  location     = {Catalina Island, CA, USA},
  pages        = {466--473},
  publisher    = {AUAI Press},
  title        = {Characterizing the set of coherent lower previsions with a finite number of constraints or vertices},
  url          = {http://event.cwi.nl/uai2010/papers/UAI2010\_0023.pdf},
  year         = {2010},
}