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.

翻译：我们提出了一个不确定性量化总框架,这是相互关联的模型的组合。我们定义了根据输入输出图的风险功能随机计算措施的全球第一和第二顺序结构和相关敏感度分析。它们是强度测量的ANOVA分解和随机测量差异的分解,每个分解到子空间。正方位随机测量提供敏感性分布。我们显示,随机计算措施可用于构建正随机字段,其中承认共变指数和敏感指数的分解,并可用于代表互动粒子系统。通过随机计算措施传播的第一和第二顺序全球敏感度分析阐明并整合了不同的不确定性量化概念,随机字段的全球敏感度分析传达了对共变的相称功能贡献。这个框架在与算法不确定性和模型选择不确定性框架结合使用时,可以补充其他参数。