Controlled stratification for quantile estimation

Claire Cannamela (1) , Josselin Garnier (2, 3, 4) , Bertrand Iooss (5, 6)

1 SUPELEC-Campus Gif
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 SIMaP - Science et Ingénierie des Matériaux et Procédés
5 LCFR - Laboratoire de Conduite et Fiabilité des Réacteurs
6 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

In this paper we propose and discuss variance reduction techniques for the estimation of quantiles of the ouput of a complex model with random input parameters. These techniques are based on the use of a reduced model, such as a metamodel or a response surface. The reduced model can be used as a control variate; or a rejection method can be implemented to sample the realizations of the input parameters in prescribed relevant strata; or the reduced model can be used to determine a good biased distribution of the input parameters for the calibration of an importance sampling strategy. The different strategies are analyzed, the asymptotic variances are computed and compared, which shows the benefit of an adaptive controlled stratification method. This method is applied to a real example (computation of the peak cladding temperature during a large-break loss of coolant accident in a nuclear reactor).

Mots clés: Quantile estimation; Monte Carlo method; Variance reduction; Computer experiments

Domaines: Méthodologie [stat.ME]; Statistiques [math.ST]; Théorie [stat.TH]

Claire Cannamela, Josselin Garnier, Bertrand Iooss. Controlled stratification for quantile estimation. Annals of Applied Statistics, 2008, 2 (4), pp.1554-1580. ⟨hal-00256644⟩