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

大多数程序标记为“经验贝叶斯”，在使用中， 目前是频率论，而不是贝叶斯;虽然往往 采用经验贝叶斯程序的动机是 类似贝叶斯的概念或计算困难 程序. 该研究拓宽了经验贝叶斯 框架，然后检查比较行为的 几种方法，就其性能和 可行性 定义条件的理论结果 将寻求经验贝叶斯方法的优越性。 模拟的经验结果和理论结果 经验贝叶斯估计量的性质将应用于 可靠性理论 统计分析利用模型或先验信息 和专家意见来建立分析数据的框架。 在 在某些情况下，数据本身可以用来确定 框架，并在框架内进行分析。 这种类型的程序被称为“经验贝叶斯”; 在某种意义上可以被看作是基于模型的 （频率论）和先验信息为基础的（贝叶斯）程序。 这项研究将调查在何种情况下，每一个 这类程序明显上级其他程序， 在可靠性测试和评估中的应用。

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.