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Characterizing coherence, correcting incoherence

Erik Quaeghebeur (UGent)
(2013) 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings. p.275-284
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Abstract
Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible.
Keywords
linear constraint, coherence, polytope, enumeration, multi-objective linear programming, incoherence, dominance, avoiding sure loss, projection

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MLA
Quaeghebeur, Erik. “Characterizing Coherence, Correcting Incoherence.” 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings, edited by Fabio Cozman et al., SIPTA, 2013, pp. 275–84.
APA
Quaeghebeur, E. (2013). Characterizing coherence, correcting incoherence. In F. Cozman, T. Denœux, S. Destercke, & T. Seidenfeld (Eds.), 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings (pp. 275–284). SIPTA.
Chicago author-date
Quaeghebeur, Erik. 2013. “Characterizing Coherence, Correcting Incoherence.” In 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings, edited by Fabio Cozman, Thierry Denœux, Sébastien Destercke, and Teddy Seidenfeld, 275–84. SIPTA.
Chicago author-date (all authors)
Quaeghebeur, Erik. 2013. “Characterizing Coherence, Correcting Incoherence.” In 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings, ed by. Fabio Cozman, Thierry Denœux, Sébastien Destercke, and Teddy Seidenfeld, 275–284. SIPTA.
Vancouver
1.
Quaeghebeur E. Characterizing coherence, correcting incoherence. In: Cozman F, Denœux T, Destercke S, Seidenfeld T, editors. 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings. SIPTA; 2013. p. 275–84.
IEEE
[1]
E. Quaeghebeur, “Characterizing coherence, correcting incoherence,” in 8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings, Compiègne, France, 2013, pp. 275–284.
@inproceedings{4099599,
  abstract     = {{Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible.}},
  author       = {{Quaeghebeur, Erik}},
  booktitle    = {{8th International Symposium on Imprecise Probability : Theories and Applications, Proceedings}},
  editor       = {{Cozman, Fabio and Denœux, Thierry and Destercke, Sébastien and Seidenfeld, Teddy}},
  isbn         = {{9782913923355}},
  keywords     = {{linear constraint,coherence,polytope,enumeration,multi-objective linear programming,incoherence,dominance,avoiding sure loss,projection}},
  language     = {{eng}},
  location     = {{Compiègne, France}},
  pages        = {{275--284}},
  publisher    = {{SIPTA}},
  title        = {{Characterizing coherence, correcting incoherence}},
  year         = {{2013}},
}