论文标题
将嵌套的蒙特卡洛索博尔的索引估计器正式化，以平衡探索和重复之间的权衡，对随机模型的全球灵敏度分析
Regularizing nested Monte Carlo Sobol' index estimators to balance the trade-off between explorations and repetitions in global sensitivity analysis of stochastic models
论文作者
论文摘要
SOBOL的随机模型的灵敏度指数估计器是嵌套蒙特卡洛估计器的函数，它们是由两个嵌套的蒙特卡洛环构建的估计器。 外循环探讨了输入空间，对于每个探索，内部循环重复模型都运行以估计有条件的期望。 尽管嵌套蒙特卡洛估计器众所周知，探索和重复的探索和重复之间的最佳分配，但尚不清楚如何处理嵌套的蒙特卡洛估计器的功能，尤其是当这些功能没有绑定的Hessian矩阵时，因为SOBOL的INDEX估计器是如此。 为了解决这个问题，引入了正则化方法，以绑定嵌套蒙特卡洛估计器功能的平均平方误差。基于启发式，提出了一种旨在最大程度地减少偏见差异权衡的分配策略。该方法应用于随机模型的SOBOL指数估计器。 在数值实验中给出并说明了一种适应模型内固有随机性水平的实用算法。
Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the explorations, the inner loop repeats model runs to estimate conditional expectations. Although the optimal allocation between explorations and repetitions of one's computational budget is well-known for nested Monte Carlo estimators, it is less clear how to deal with functions of nested Monte Carlo estimators, especially when those functions have unbounded Hessian matrices, as it is the case for Sobol' index estimators. To address this problem, a regularization method is introduced to bound the mean squared error of functions of nested Monte Carlo estimators. Based on a heuristic, an allocation strategy that seeks to minimize a bias-variance trade-off is proposed. The method is applied to Sobol' index estimators for stochastic models. A practical algorithm that adapts to the level of intrinsic randomness in the models is given and illustrated on numerical experiments.
