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ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Lev Utkin, Sebastien Destercke

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

### Abstract

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.

** Keywords. ** P-boxes, Random Sets, Linear programming, Lower/upper expectation, Optimization

** Paper Download **

The paper is availabe in the following formats:

** Authors addresses: **

Lev Utkin

Institutski per. 5, 194021 St.Petersburg

Sebastien Destercke

CE Cadarache, bat 702

13115 Saint-Paul-Lez-Durance CEDEX

** E-mail addresses: **

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