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Computing expectations with p-boxes: two views of the same problem


Congress title :5th international symposium on imprecise probabilities : theory and application (ISIPTA)
Congress town :Prague
Congress date :16/07/2007

Document type > *Congrès/colloque

Keywords > linear programming, lower/upper expectation, optimization, p-boxes, random sets

Research Unit > IRSN/DPAM/SEMIC/LIMSI

Authors > DESTERCKE Sébastien, UTKIN Lev

Publication Date > 19/07/2007

Summary

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 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.

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