A comprehensive comparison of total-order estimators for global sensitivity analysis

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal for Uncertainty Quantification Pub Date : 2020-09-02 DOI:10.1615/Int.J.UncertaintyQuantification.2021038133

A. Puy, W. Becker, S. L. Piano, Andrea Saltelli

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引用次数: 19

Abstract

Sensitivity analysis helps identify which model inputs convey the most uncertainty to the model output. One of the most authoritative measures in global sensitivity analysis is the Sobol' total-order index, which can be computed with several different estimators. Although previous comparisons exist, it is hard to know which estimator performs best since the results are contingent on the benchmark setting defined by the analyst (the sampling method, the distribution of the model inputs, the number of model runs, the test function or model and its dimensionality, the weight of higher order effects or the performance measure selected). Here we compare several total-order estimators in an eight-dimension hypercube where these benchmark parameters are treated as random parameters. This arrangement significantly relaxes the dependency of the results on the benchmark design. We observe that the most accurate estimators are Razavi and Gupta's, Jansen's or Janon/Monod's for factor prioritization, and Jansen's, Janon/Monod's or Azzini and Rosati's for approaching the"true"total-order indices. The rest lag considerably behind. Our work helps analysts navigate the myriad of total-order formulae by reducing the uncertainty in the selection of the most appropriate estimator.

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用于全局灵敏度分析的全阶估计量的综合比较

敏感性分析有助于确定哪些模型输入向模型输出传递了最大的不确定性。全局灵敏度分析中最权威的度量之一是Sobol的全阶指数，它可以用几种不同的估计量来计算。尽管存在先前的比较，但很难知道哪个估计器表现最好，因为结果取决于分析师定义的基准设置（采样方法、模型输入的分布、模型运行的次数、测试函数或模型及其维度、高阶效应的权重或所选的性能度量）。在这里，我们比较了八维超立方体中的几个全阶估计量，其中这些基准参数被视为随机参数。这种安排显著地放松了结果对基准设计的依赖性。我们观察到，最准确的估计量是Razavi和Gupta的、Jansen的或Janon/Monod的因子优先级，以及Jansen的、Janon/Manod的或Azzini和Rosati的接近“真实”总序指数的估计量。其余的大大落后了。我们的工作通过减少选择最合适估计量的不确定性，帮助分析师浏览无数的总阶公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.