论文标题
通过随机测量和场的不确定性定量
Uncertainty Quantification by Random Measures and Fields
论文作者
论文摘要
我们提出了一个不确定性定量的一般框架，该框架是互连模型的镶嵌物。我们为在投入输出图的风险功能上的随机计数量度定义了全局一阶和二阶结构和相关敏感性分析。这些是强度度量的ANOVA分解和随机度量方差的分解，每个方差分为子空间。正交随机测量提供灵敏度分布。我们表明，随机计数度量可用于构建正随机场，该场允许协方差和灵敏度指数的分解，并可用于表示相互作用的粒子系统。通过随机计数衡量的一阶和二阶全局灵敏度分析阐明并整合了不确定性定量的不同概念，而随机场的全局灵敏度分析传达了对协方差的比例功能贡献。当与算法不确定性和模型选择不确定性框架结合使用时，该框架会补充其他框架。
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk functionals of input-output maps. These are the ANOVA decomposition of the intensity measure and the decomposition of the random measure variance, each into subspaces. Orthogonal random measures furnish sensitivity distributions. We show that the random counting measure may be used to construct positive random fields, which admit decompositions of covariance and sensitivity indices and may be used to represent interacting particle systems. The first and second order global sensitivity analyses conveyed through random counting measures elucidate and integrate different notions of uncertainty quantification, and the global sensitivity analysis of random fields conveys the proportionate functional contributions to covariance. This framework complements others when used in conjunction with for instance algorithmic uncertainty and model selection uncertainty frameworks.
