马氏核的条件期望及其在统计推断和疾病诊断中的应用
Conditional Expectation of a Markov Kernel Given Another with Some Applications in Statistical Inference and Disease Diagnosis
摘要：
马尔可夫核在概率论和数理统计理论中起着决定性的作用，是σ域和统计概念的推广。独立性、充分性、完备性、辅助性或条件分布等概念以前已经扩展到马尔可夫核。本文引入了马尔可夫核给定另一个马尔可夫核的条件期望的概念，给出了它的第一个性质。提供了一种临床诊断的应用，获得了诊断测试的预测值的最优性。在一个统计框架中，这个新的概率工具被用来扩展到马尔可夫核的定理{Rao-Blackwell}和Lehmann-Scheffé。通过适当扩大概率族，顺便得到了一个关于充分统计量完备性的结果。作为统计学的最后一章，给出了非随机估计族完备性的一个结果的推广。
英文摘要：
Markov kernels play a decisive role in probability and mathematical statistics theories, and are an extension of the concepts of sigma-field and statistic. Concepts such as independence, sufficiency, completeness, ancillarity or conditional distribution have been extended previously to Markov kernels. In this paper, the concept of conditional expectation of a Markov kernel given another is introduced, setting its first properties. An application to clinical diagnosis is provided, obtaining {an} optimality property of the predictive values of a diagnosis test. In a statistical framework, this new probabilistic tool is used to extend to Markov kernels the theorems of {Rao-Blackwell} and Lehmann-Scheffé. A result about the completeness of a sufficient statistic is obtained in passing by properly enlarging the family of probabilities. As a final statistical scholium, a generalization of a result about the completeness of the family of nonrandomized estimators is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
