This paper introduces a new mathematical object: the confidence structure. A confidence structure represents inferential uncertainty in an unknown parameter by defining a belief function whose output is commensurate with Neyman-Pearson confidence. Confidence structures on a group of input variables can be propagated through a function to obtain a valid confidence structure on the output of that function. The theory of confidence structures is created by enhancing the extant theory of confidence distributions with the mathematical generality of Dempster-Shafer evidence theory. Mathematical proofs grounded in random set theory demonstrate the operative properties of confidence structures. The result is a new theory which achieves the holistic goals of Bayesian inference while maintaining the empirical rigor of frequentist inference.

中文翻译：

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置信结构理论的数学基础

本文介绍了一个新的数学对象：置信结构。置信结构通过定义输出与 Neyman-Pearson 置信度相称的置信函数来表示未知参数的推论不确定性。一组输入变量的置信结构可以通过一个函数传播，以获得该函数输出的有效置信结构。置信结构理论是通过用 Dempster-Shafer 证据理论的数学普遍性增强现有的置信分布理论而创建的。以随机集理论为基础的数学证明证明了置信结构的操作特性。结果是一个新的理论，它实现了贝叶斯推理的整体目标，同时保持了频率论推理的经验严谨性。