Adaptive Design of Experiments for Conservative Estimation of Excursion Sets (SIAM UQ 2016)

Dario Azzimonti (1, 2) , David Ginsbourger (1, 3, 2) , Clément Chevalier (4, 2) , Julien Bect (5, 2) , Yann Richet (6, 2)

1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 IDIAP Research Institute
4 UNINE - Université de Neuchâtel
5 L2S - Laboratoire des signaux et systèmes
6 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

We consider a Gaussian process model trained on few evaluations of an expensive to evaluate deterministic function and we study the problem of estimating a fixed excursion set of this function. We focus on conservative estimates of the excursion set and we present a method based on Vorob'ev quantiles, that sequentially selects new evaluations of the function in order to reduce the uncertainty on the estimate. The method is then applied to a test case.

Domains: Computation [stat.CO]

Dario Azzimonti, David Ginsbourger, Clément Chevalier, Julien Bect, Yann Richet. Adaptive Design of Experiments for Conservative Estimation of Excursion Sets (SIAM UQ 2016). 2016 SIAM Conference on Uncertainty Quantification, Apr 2016, Lausanne, Switzerland. ⟨hal-01329571⟩