Sequential experimental Design for Misspecified Nonlinear Models

Hassan El Abiad (1) , Laurent Le Brusquet (1) , Marie-Eve Davoust (1)

1 SUPELEC-Campus Gif

In design of experiments for nonlinear regression model identification, the design criterion depends on the unknown parameters to be identified. Classical strategies consist in designing sequentially the experiments by alternating the estimation and design stages. These strategies consider previous observations (collected data) only while estimating the unknown parameters during the estimation stages. This paper proposes to consider the previous observations not only during the estimation stages, but also by the criterion used during the design stages. Furthermore, the proposed criterion considers the robustness requirement: an unknown model error (misspecification) is supposed to exist and is modeled by a kernel-based representation (Gaussian process). Finally, the proposed sequential criterion is compared with a model-robust criterion which does not consider the previously collected data during the design stages, with the classical D-optimal and L-optimal criteria.

Mots clés: Sequential design of experiments; Gaussian process; Nonlinear regression; Robust design; Parameters identification.; Parameters identification

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]; Autres [stat.ML]

Hassan El Abiad, Laurent Le Brusquet, Marie-Eve Davoust. Sequential experimental Design for Misspecified Nonlinear Models. IEEE-ICASSP International Conference on Acoustics, Speech and Signal Processing, Apr 2008, Las Vegas, United States. pp. 3609-3612, ⟨10.1109/ICASSP.2008.4518433⟩. ⟨hal-00273815⟩