Title: BIMC: The Bayesian Inverse Monte Carlo method for goal-oriented uncertainty quantification. Part I Show Chinese title

Title: BIMC: 用于目标不确定性量化的目标逆蒙特卡洛方法。 第一部分

Abstract: We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling algorithms such as the Monte Carlo method may require infeasible running times to accurately evaluate these probabilities. We propose an importance sampling scheme (which we call BIMC) that relies on solving an auxiliary, fictitious Bayesian inverse problem. The solution of the inverse problem yields a posterior PDF, a local Gaussian approximation to which serves as the importance sampling density. We apply BIMC to several problems and demonstrate that it can lead to computational savings of several orders of magnitude over the Monte Carlo method. We delineate conditions under which BIMC is optimal, as well as conditions when it can fail to yield an effective IS density. Show Chinese abstract

Abstract: 我们研究了估计罕见事件概率的问题，重点关注那些受带有不确定输入参数的微分方程支配的系统。 如果系统动力学计算昂贵，标准的采样算法（例如蒙特卡罗方法）可能需要不可行的运行时间来准确评估这些概率。 我们提出了一种重要性抽样方案（我们称之为BIMC），该方案依赖于求解一个辅助的、虚构的贝叶斯逆问题。 逆问题的解会产生一个后验PDF，其局部高斯近似用作重要性抽样密度。 我们将BIMC应用于多个问题，并证明它可以比蒙特卡罗方法带来几个数量级的计算节省。 我们界定了BIMC最优的条件，以及它可能无法产生有效的重要性抽样密度的条件。