Set estimation, computation of volumes and data safety

Isabelle Braems (1) , Luc Jaulin (2, 3, 4) , Michel Kieffer (5, 6, 7) , Eric Walter (5)

1 LEMHE - Laboratoire d'étude des matériaux hors équilibre
2 STIC - Département STIC [Brest]
3 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
4 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
5 L2S - Laboratoire des signaux et systèmes
6 LTCI - Laboratoire Traitement et Communication de l'Information
7 IUF - Institut universitaire de France

This paper proposes a new method for bracketing a set S defined by nonlinear inequalities between an inner set S- and an outer set S+. Contrary to eixting approaches for which S- and S+ are unions of boxes, these two sets are defined as unions of polytopes. This characterization makes it possible to describe S and compute its volume in a more accurate way than with classical methods. The resulting approach is used to quantify the influence of a given interval datum in parameter estimation, whan the feasible set for the parameters is defined as the set of all parameters vectors consistent with all intervall data. In order to detect potential outliers, we characterize the influence of any given datum on this set by its safety defined as the ratio between the volumes of the feasible sets computed with and without this datum. This problem amounts to computing volumes of sets as acurately as possible.

Mots clés: Bounded errors; outlier; parameter identification; set estimation

Domaines: Sciences de l'ingénieur [physics]

Isabelle Braems, Luc Jaulin, Michel Kieffer, Eric Walter. Set estimation, computation of volumes and data safety. SCAN-Interval 2000, Sep 2000, Karlsrhue, Germany. pp.267-280. ⟨hal-00845041⟩