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Metafunctions for benchmarking in sensitivity analysis

机译：用于敏感性分析中的基准测试的元功能

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摘要

Comparison studies of global sensitivity analysis (GSA) approaches are limited in that they are performed on a single model or a small set of test functions, with a limited set of sample sizes and dimensionalities. This work introduces a flexible 'metafunction' framework to benchmarking which randomly generates test problems of varying dimensionality and functional form using random combinations of plausible basis functions, and a range of sample sizes. The metafunction is tuned to mimic the characteristics of real models, in terms of the type of model response and the proportion of active model inputs. To demonstrate the framework, a comprehensive comparison of ten GSA approaches is performed in the screening setting, considering functions with up to 100 dimensions and up to 1000 model runs. The methods examined range from recent metamodelling approaches to elementary effects and Monte Carlo estimators of the Sobol' total effect index. The results give a comparison in unprecedented depth, and show that on average and in the setting investigated, Monte Carlo estimators, particularly the VARS estimator, outperform metamodels. Indicatively, metamodels become competitive at around 10-20 runs per model input, but at lower ratios sampling-based approaches are more effective as a screening tool.
机译：全局敏感性分析（GSA）方法的比较研究是有限的，因为它们是在单个模型或一小组测试功能上进行的，具有有限的样本尺寸和尺寸。这项工作将灵活的“元功能”框架引入了基准测试，该基准测试使用可编合理的基本功能的随机组合以及一系列样本尺寸的随机组合随机产生不同维度和功能形式的测试问题。在模型响应类型和有源模型输入的比例方面，调整元件以模仿真实模型的特征。为了展示框架，在筛选设置中执行10个GSA方法的全面比较，考虑到多达100个维度和高达1000个模型运行的函数。该方法研究了最近的元素效应和蒙特卡罗估算的基本效应指数的源自效应和蒙特卡罗估算。结果在前所未有的深度中进行了比较，并显示平均而且在设置调查，蒙特卡罗估计器，特别是vars估计器，优于变形的元模型。标识地，元模型在每种型号输入的10-20次左右变得竞争，但在较低的比率下，基于样品的方法更有效地作为筛选工具。

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