Mathematical Foundations for a Theory of Confidence Structures.
Mathematical Foundations for a Theory of Confidence Structures.
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置信结构理论的数学基础。
DOI：
10.1016/j.ijar.2012.05.006
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Balch,MichaelScott
中科院分区：
文献类型：
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作者：
Balch,MichaelScott
本文介绍了一种新的数学对象：置信结构。置信度结构通过定义一个置信函数来表示未知参数中的推理不确定性，该置信函数的输出与Neyman-Pearson置信度相称。一组输入变量的置信度结构可以通过函数传播，以获得该函数输出的有效置信度结构。置信度结构理论是在现有的置信度分布理论基础上，利用Dempster-Shafer证据理论的数学一般性而建立起来的。基于随机集理论的数学证明证明了置信结构的操作性质。结果是一个新理论，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。
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.