%0 Conference Proceedings
%T Computing expectations with p-boxes: two views of the same problem
%+ Department of computer science, St Petersburg Forest Technical Academy
%+ Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
%+ Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA)
%A Utkin, Lev
%A Destercke, Sébastien
%< avec comité de lecture
%( Proceedings of the fifth international symposium on imprecise probability: theories and applications
%( Proceedings of the fifth international symposium on imprecise probability: theories and applications
%B The fifth international symposium on imprecise probability: theories and applications
%C Prague, Czech Republic
%P 435-445
%8 2007
%D 2007
%K P-boxes
%K Random Sets
%K Linear programming
%K Lower/upper expectation
%K Optimization
%Z Computer Science [cs]/Other [cs.OH]
%Z Mathematics [math]/Probability [math.PR]Conference papers
%X Given an imprecise probabilistic model over a continuous space, computing lower (upper) expectations is often computationally hard to achieve, even in simple cases. Building tractable methods to do so is thus a crucial point in applications. In this paper, we concentrate on p-boxes (a simple and popular model), and on lower expectations computed over non-monotone functions. For various particular cases, we propose tractable methods to compute approximations or exact values of these lower expectations. We found interesting to put in evidence and to compare two approaches: the first using general linear programming, and the second using the fact that p-boxes are special cases of random sets. We underline the complementarity of both approaches, as well as the differences.
%G English
%2 https://irsn.hal.science/irsn-00196687/document
%2 https://irsn.hal.science/irsn-00196687/file/ISIPTA07_UtkDes_Preprint.pdf
%L irsn-00196687
%U https://irsn.hal.science/irsn-00196687
%~ IRSN
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ INSMI
%~ UT1-CAPITOLE
%~ IRIT
%~ IRIT-ADRIA
%~ IRIT-IA
%~ TOULOUSE-INP
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP