Bayesian Subset Simulation: a kriging-based subset simulation algorithm for the estimation of small probabilities of failure

Ling Li (1) , Julien Bect (2, 1) , Emmanuel Vazquez (1)

1 E3S - Supélec Sciences des Systèmes
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au \& Beck (Prob. Eng. Mech., 2001) has become one of the most popular method to solve it. Subset simulation has been shown to provide significant savings in the number of simulations to achieve a given accuracy of estimation, with respect to many other Monte Carlo approaches. The number of simulations remains still quite high however, and this method can be impractical for applications where an expensive-to-evaluate computer model is involved. We propose a new algorithm, called Bayesian Subset Simulation, that takes the best from the Subset Simulation algorithm and from sequential Bayesian methods based on kriging (also known as Gaussian process modeling). The performance of this new algorithm is illustrated using a test case from the literature. We are able to report promising results. In addition, we provide a numerical study of the statistical properties of the estimator.

Mots clés: Subset Simulation; Probability of failure; Sequential design; Computer experiments

Domaines: Calcul [stat.CO]

Ling Li, Julien Bect, Emmanuel Vazquez. Bayesian Subset Simulation: a kriging-based subset simulation algorithm for the estimation of small probabilities of failure. 11th International Probabilistic Assessment and Management Conference (PSAM11) and The Annual European Safety and Reliability Conference (ESREL 2012), Jun 2012, Helsinki, Finland. CD-ROM Proceedings (10 p.). ⟨hal-00715316⟩