论文标题
具有顺序定向重要性采样（SDI）的罕见事件估计
Rare event estimation with sequential directional importance sampling (SDIS)
论文作者
论文摘要
在本文中，我们提出了一种顺序定向重要性采样（SDIS）方法，以进行罕见的事件估计。 SDI以辅助故障概率的序列而表达了很小的故障概率，该概率是通过放大输入变异性来定义的。序列中的第一个概率是通过登录坐标中的蒙特卡洛模拟来估计的，并且所有后续坐标都以极地坐标中的方向重要性采样计算。来自用于估计中间概率的定向重要性采样密度的样本通过重新样本移动方案以顺序绘制中间概率。后者在笛卡尔坐标中方便地进行，并通过合适的转换获得方向样品。在移动步骤中，我们讨论了两个马尔可夫链蒙特卡洛（MCMC）算法，用于在低维问题中应用。最后，提出了定义中间故障概率的参数的自适应选择，并分析了故障概率估计的变异系数。在各种问题设置中，对五个示例进行了测试，该方法测试了该方法表明该方法的表现优于现有的顺序采样可靠性方法。
In this paper, we propose a sequential directional importance sampling (SDIS) method for rare event estimation. SDIS expresses a small failure probability in terms of a sequence of auxiliary failure probabilities, defined by magnifying the input variability. The first probability in the sequence is estimated with Monte Carlo simulation in Cartesian coordinates, and all the subsequent ones are computed with directional importance sampling in polar coordinates. Samples from the directional importance sampling densities used to estimate the intermediate probabilities are drawn in a sequential manner through a resample-move scheme. The latter is conveniently performed in Cartesian coordinates and directional samples are obtained through a suitable transformation. For the move step, we discuss two Markov Chain Monte Carlo (MCMC) algorithms for application in low and high-dimensional problems. Finally, an adaptive choice of the parameters defining the intermediate failure probabilities is proposed and the resulting coefficient of variation of the failure probability estimate is analyzed. The proposed SDIS method is tested on five examples in various problem settings, which demonstrate that the method outperforms existing sequential sampling reliability methods.
