Characterizing the set of coherent lower previsions with a finite number of constraints or vertices
- Author
- Erik Quaeghebeur (UGent)
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-984156
- 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, edited by Peter Grünwald and Peter Spirtes, AUAI Press, 2010, pp. 466–73.
- 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). Corvallis, OR, USA: AUAI Press.
- Chicago author-date
- 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, edited by Peter Grünwald and Peter Spirtes, 466–73. Corvallis, OR, USA: AUAI Press.
- Chicago author-date (all authors)
- 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 by. Peter Grünwald and Peter Spirtes, 466–473. 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.
- IEEE
- [1]E. Quaeghebeur, “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, Catalina Island, CA, USA, 2010, pp. 466–473.
@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 = {{Grünwald, Peter and Spirtes, Peter}},
isbn = {{9780974903965}},
keywords = {{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}},
}