Mathematical Sciences: Contributions to the Theory and Methods of Empirical Bayes Estimation

目前使用的大多数被标记为“经验贝叶斯”的程序是频繁的而不是贝叶斯的；尽管使用经验贝叶斯程序的动机通常是类似的贝叶斯程序的概念或计算困难。本研究扩展了经验贝叶斯框架，考察了几种方法在绩效和可行性方面的比较行为。将寻求定义经验贝叶斯方法优势条件的理论结果。模拟的经验结果和关于经验贝叶斯估计性质的理论结果将被应用于可靠性理论。统计分析利用模型或先验信息和专家意见来确定分析数据的框架。在某些情况下，数据本身可用于确定框架以及在框架内进行分析。这种类型的过程被称为“经验贝叶斯”；在某种意义上，这些过程可以被视为基于模型(频率)和基于先验信息(贝叶斯)的过程的混合体。这项研究将调查在可靠性测试和估计应用中，每一类程序明显优于其他程序的情况。

Most procedures labeled "Empirical Bayes" that are in use at present are frequentist rather than Bayesian; although often the motivation for employing Empirical Bayes procedures is the conceptual or the computational difficulty of the analogous Bayes procedures. This research broadens the Empirical Bayes framework and then examines the comparative behaviors of the several methodologies with respect their performance and their feasibility. Theoretical results defining conditions of superiority for Empirical Bayes methods will be sought. Empirical results from simulations and theoretical results for properties of Empirical Bayes estimators will be applied to reliability theory. Statistical analyses draw on models or on prior information and expert opinion to set the framework for analyzing data. In certain circumstances the data itself can be used to determine the framework as well as be analyzed within the framework. Procedures of this type are called "Empirical Bayes;" and these can be viewed in some sense as a hybrid of model-based (frequentist) and prior information-based (Bayesian) procedures. This research will investigate the circumstances under which each class of procedures is significantly superior to the others for applications in reliability testing and estimation.