Bayesian subset simulation

Abstract : We consider the problem of estimating a probability of failure $\alpha$, defined as the volume of the excursion set of a function $f:\mathbb{X} \subseteq \mathbb{R}^{d} \to \mathbb{R}$ above a given threshold, under a given probability measure on $\mathbb{X}$. In this article, we combine the popular subset simulation algorithm (Au and Beck, Probab. Eng. Mech. 2001) and our sequential Bayesian approach for the estimation of a probability of failure (Bect, Ginsbourger, Li, Picheny and Vazquez, Stat. Comput. 2012). This makes it possible to estimate $\alpha$ when the number of evaluations of $f$ is very limited and $\alpha$ is very small. The resulting algorithm is called Bayesian subset simulation (BSS). A key idea, as in the subset simulation algorithm, is to estimate the probabilities of a sequence of excursion sets of $f$ above intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A Gaussian process prior on $f$ is used to define the sequence of densities targeted by the SMC algorithm, and drive the selection of evaluation points of $f$ to estimate the intermediate probabilities. Adaptive procedures are proposed to determine the intermediate thresholds and the number of evaluations to be carried out at each stage of the algorithm. Numerical experiments illustrate that BSS achieves significant savings in the number of function evaluations with respect to other Monte Carlo approaches.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [52 references]  Display  Hide  Download
Contributor : Julien Bect <>
Submitted on : Wednesday, August 23, 2017 - 4:16:36 PM
Last modification on : Thursday, April 5, 2018 - 12:30:05 PM


Publisher files allowed on an open archive



Julien Bect, Ling Li, Emmanuel Vazquez. Bayesian subset simulation. SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2017, 5 (1), pp.762-786. ⟨⟩. ⟨10.1137/16M1078276⟩. ⟨hal-01253706v4⟩



Record views


Files downloads