标题： 贝叶斯子集模拟：一种基于克里金的子集模拟算法，用于小失效概率的估计 显示英文标题

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

摘要： 从计算机模拟中估计小失效概率是工程中的一个经典问题，Au 和 Beck（《工程力学概率》，2001年）提出的子集模拟算法已成为解决该问题的最流行方法之一。研究表明，与许多其他蒙特卡罗方法相比，子集模拟在达到给定精度估计时所需的模拟次数显著减少。然而，所需的模拟次数仍然相当高，因此对于涉及昂贵计算模型的应用来说可能不切实际。我们提出了一种新的算法，称为贝叶斯子集模拟算法，它结合了子集模拟算法和基于克里金法（也称高斯过程建模）的序贯贝叶斯方法的优点。通过文献中的一个测试案例展示了这种新算法的性能，并报告了有前景的结果。此外，我们还研究了估计器的统计性质。 显示英文摘要

摘要： 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.