Global sensitivity analysis provides insight into how sources of uncertainty contribute to uncertainty in predictions of computational models. Global sensitivity indices, also called variance-based sensitivity indices and Sobol indices, are most often computed with Monte Carlo methods. However, when the computational model is computationally expensive and only a small number of samples can be generated, that is, in so-called small-data settings, usual Monte Carlo estimates may lack sufficient accuracy. As a means of improving accuracy in such small-data settings, we explore the use of probabilistic learning. The objective of the probabilistic learning is to learn from the available samples a probabilistic model that can be used to generate additional samples, from which Monte Carlo estimates of the global sensitivity indices are then deduced. We demonstrate the interest of such a probabilistic learning method by applying it in an illustration concerned with forecasting the contribution of the Antarctic ice sheet to sea-level rise.

中文翻译：

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通过流形上的概率学习从小数据集计算全局敏感性分析中的 Sobol 指数

全局敏感性分析提供了对不确定性来源如何导致计算模型预测中的不确定性的洞察。全局敏感度指数，也称为基于方差的敏感度指数和 Sobol 指数，最常使用蒙特卡罗方法计算。但是，当计算模型的计算量很大，并且只能生成少量样本时，即在所谓的小数据设置中，通常的蒙特卡罗估计可能缺乏足够的准确性。作为在这种小数据设置中提高准确性的一种手段，我们探索了概率学习的使用。概率学习的目标是从可用样本中学习一个概率模型，该模型可用于生成额外的样本，然后从中推导出全局敏感性指数的蒙特卡罗估计。