基于广义Lambda代理模型的随机模拟器全局敏感性分析
Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models
摘要：
全局敏感性分析旨在量化输入变量对计算模型响应变量的影响。它已被广泛应用于确定性仿真器，其中一组输入参数具有唯一对应的输出值。然而，随机模拟器由于使用（伪）随机数而具有内在随机性，因此当使用相同的输入参数但使用非常见的随机数运行两次时，它们会给出不同的结果。由于这种随机性，用于全局敏感性分析的传统Sobol指数可以以不同的方式扩展到随机模拟器。在本文中，我们讨论了三种可能的扩展，并专注于那些只依赖于输入和输出之间的统计依赖。这种选择忽略了涉及内部随机性的详细数据生成过程，因此可以应用于更广泛的问题。我们建议使用广义lambda模型来模拟随机模拟器的响应分布。这样的代理可以在不需要复制的情况下构造。所提出的方法被应用到三个例子，包括两个案例研究在金融和流行病学。结果证实了收敛的方法估计的灵敏度指数，即使存在强异方差和小的信号噪声比。
英文摘要：
Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a unique corresponding output value. Stochastic simulators, however, have intrinsic randomness due to their use of (pseudo)random numbers, so they give different results when run twice with the same input parameters but non-common random numbers. Due to this random nature, conventional Sobol' indices, used in global sensitivity analysis, can be extended to stochastic simulators in different ways. In this paper, we discuss three possible extensions and focus on those that depend only on the statistical dependence between input and output. This choice ignores the detailed data generating process involving the internal randomness, and can thus be applied to a wider class of problems. We propose to use the generalized lambda model to emulate the response distribution of stochastic simulators. Such a surrogate can be constructed without the need for replications. The proposed method is applied to three examples including two case studies in finance and epidemiology. The results confirm the convergence of the approach for estimating the sensitivity indices even with the presence of strong heteroskedasticity and small signal-to-noise ratio.
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