  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.
