Computing Expectations with Continuous P-Boxes: Univariate Case

TL;DR

This paper addresses the challenge of computing lower expectations in imprecise probabilistic models, specifically p-boxes, by proposing two approaches for the univariate case to improve computational tractability.

Contribution

It introduces and compares two methods—linear programming and random set representation—for calculating expectations with p-boxes in the univariate case.

Findings

Linear programming approach is effective for lower expectations.

Random set approach offers complementary advantages.

Both methods enhance computational efficiency for p-box models.

Abstract

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.