Computing Expectations with Continuous P-Boxes: Univariate Case

Details Computing Expectations with Continuous P-Boxes: Univariate Case Computing Expectations with Continuous P-Boxes: Univariate Case

2009-06-06

arxiv.org/abs/0906.1260v1

International Journal of Approximate Reasoning, Vol 50, n 5, pp 778-798, 2009

Mathematics

Probability

31 pages, 6 figures, constitute an extended version of a small paper accepted in ISIPTA conference, and a preprint version of

Scientific paper

10.1016/j.ijar.2009.02.004

Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis, tractable methods to compute them are crucial in many applications involving imprecise probabilistic models. We concentrate on p-boxes (a simple and popular model), and on the computation of lower expectations of non-monotone functions. This paper is devoted to the univariate case, that is where only one variable has uncertainty. We propose and 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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