Computing Expectations with Continuous P-Boxes: Univariate Case

• Main Authors: Utkin, L, Destercke, S
• Format: Journal Article
• Language: English
• Published: 06-06-2009
• Subjects: Mathematics - Probability; Mathematics - Statistics Theory; Statistics - Theory
• DOI: 10.48550/arxiv.0906.1260

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