Variance-based sensitivity indices play an important role in scientific computation and data mining, thus the significance of developing numerical methods for efficient and reliable estimation of these sensitivity indices based on (expensive) computer simulators and/or data cannot be emphasized too much. In this article, the estimation of these sensitivity indices is treated as a statistical inference problem. Two principle lemmas are first proposed as rules of thumb for making the inference. After that, the posterior features for all the (partial) variance terms involved in the main and total effect indices are analytically derived (not in closed form) based on Bayesian Probabilistic Integration (BPI). This forms a data-driven method for estimating the sensitivity indices as well as the involved discretization errors. Further, to improve the efficiency of the developed method for expensive simulators, an acquisition function, named Posterior Variance Contribution (PVC), is utilized for realizing optimal designs of experiments, based on which an adaptive BPI method is established. The application of this framework is illustrated for the calculation of the main and total effect indices, but the proposed two principle lemmas also apply to the calculation of interaction effect indices. The performance of the development is demonstrated by an illustrative numerical example and three engineering benchmarks with finite element models.

基于方差的敏感度指数在科学计算和数据挖掘中发挥着重要作用，因此基于（昂贵的）计算机模拟器和/或数据开发用于有效和可靠估计这些敏感度指数的数值方法的重要性再怎么强调也不为过。在本文中，这些敏感性指标的估计被视为统计推理问题。首先提出了两个原则引理作为进行推理的经验法则。之后，基于贝叶斯概率积分 (BPI) 分析导出（非封闭形式）主效应指标和总效应指标中涉及的所有（部分）方差项的后验特征。这形成了一种数据驱动的方法，用于估计敏感度指数以及所涉及的离散化误差。更多，为了提高昂贵模拟器开发方法的效率，利用名为后验方差贡献（PVC）的采集函数来实现实验的优化设计，在此基础上建立了自适应 BPI 方法。该框架的应用说明了主要和总效应指数的计算，但提出的两个原则引理也适用于相互作用效应指数的计算。开发的性能通过一个说明性的数值例子和三个带有有限元模型的工程基准来证明。该框架的应用说明了主要和总效应指数的计算，但提出的两个原则引理也适用于相互作用效应指数的计算。开发的性能通过一个说明性的数值例子和三个带有有限元模型的工程基准来证明。该框架的应用说明了主要和总效应指数的计算，但提出的两个原则引理也适用于相互作用效应指数的计算。开发的性能通过一个说明性的数值例子和三个带有有限元模型的工程基准来证明。