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

目前使用的大多数标记为“经验贝叶斯”的程序都是频率主义者而不是贝叶斯主义者；尽管通常采用经验贝叶斯过程的动机是类似贝叶斯过程的概念或计算难度。本研究扩大了实证贝叶斯框架，然后从性能和可行性方面考察了几种方法的比较行为。将寻求确定经验贝叶斯方法优越性条件的理论结果。模拟的经验结果和经验贝叶斯估计器性质的理论结果将应用于可靠性理论。统计分析利用模型或先验信息和专家意见来设置分析数据的框架。在某些情况下，数据本身可以用来确定框架，也可以在框架内进行分析。这种类型的过程被称为“经验贝叶斯”；在某种意义上，这些可以被视为基于模型（频率主义者）和基于先验信息（贝叶斯）过程的混合体。本研究将探讨在可靠性测试和估计的应用中，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.