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Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

机译：使用Bayesian Multimodel推论和重要性采样来确定全局敏感性分析

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Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol') indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. We propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol' index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol' indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol' indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol' indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol' indices converge to the true/deterministic Sobol' indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.
机译：全球敏感性分析（GSA）旨在了解不确定输入变量对模型响应的相对重要性。传统的GSA涉及计算具有已知模型参数分布的模型的灵敏度（Sobol'）索引。然而，模型参数受到杀菌和认知不确定性的影响，后者通常由缺乏数据引起的。我们提出了一种新的框架，以量化概率模型 - 形式的不确定性和由小型数据集产生的模型参数，并将这些不确定性集成到Sobol'指数估计中。首先，该过程通过贝叶斯多模型推断建立了一组候选概率模型及其相关概率。使用重要的采样重新重量方法，从这些概率模型计算不精确的索尔索引。这导致概率的Sobol'指数，其分布表征了由小型数据集大小产生的灵敏度的不确定性。因此，不精确的Sobol'指数因此为敏感性估计提供了令人信心的衡量标准，而且，可以用于通知数据收集努力，以最大限度地减少不确定性的影响。通过研究Timoshenko波束参数的示例，我们认为这些概率索波尔的指数随着数据集大小的增加而汇集到真正/确定性的Sobol'索引，因此，分布形式不确定性降低。然后应用该方法以评估E-玻璃纤维复合材料外平面性质与其组成性质的敏感性。该第二示例说明了当缺少某些输入参数时具有宽范围应用的重要应用的重要材料的方法。

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