SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2062-A2087, January 2020.
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial differential equation (PDE). Since numerical evaluations of PDEs are computationally expensive, estimating such probabilities of failure by Monte Carlo sampling is intractable. We develop a novel estimator based on a sequential importance sampler using discretizations of PDE-based limit state functions with different accuracies. A twofold adaptive algorithm ensures that we obtain an estimate based on the desired discretization accuracy. Moreover, we suggest and study the choice of the Markov chain Monte Carlo kernel for use with sequential importance sampling. Instead of the popular adaptive conditional sampling method, we propose a new algorithm that uses independent proposals from an adaptively constructed von Mises--Fisher--Nakagami distribution.

中文翻译：

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用于稀有事件估计的多级顺序重要性采样

SIAM科学计算杂志，第42卷，第4期，第A2062-A2087页，2020年1月。
罕见事件概率的估计是可靠性和风险评估中的重要任务。我们考虑以极限状态函数表示的故障事件，该极限状态函数取决于偏微分方程（PDE）的解。由于PDE的数值评估在计算上是昂贵的，因此难以通过蒙特卡洛采样来估计这种失败的可能性。我们使用具有不同精度的基于PDE的极限状态函数的离散化，基于顺序重要性采样器开发了一种新颖的估计器。双重自适应算法可确保我们根据所需的离散化精度获得估算值。此外，我们建议并研究马尔可夫链蒙特卡洛核的选择，以用于顺序重要性抽样。代替流行的自适应条件采样方法，