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

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