Collaborative Research: Empirical and Hierarchical Bayesian Methods with Applications to Small Area Estimation

该项目将引入一些新的实证和层次贝叶斯（EB和HB）方法，这些方法可用于人口统计学、社会学、商业、保险、经济学和调查等领域的广泛问题。特别是，这些方法有望很容易地适用于涉及离散和连续数据的某些小面积估计问题。本研究的两个主要激励例子是对少数族裔亚人群未投保比例的估计，以及对患有临床抑郁症的非裔美国女性比例的社区水平估计。第一个主题与许多联邦机构，如疾病控制中心/国家卫生统计中心和美国人口普查局有着巨大的相关性。二是与从事家庭与社区健康研究的研究人员直接相关。该项目预计将开发一种通用的EB置信区间，不仅适用于连续数据，也适用于离散数据，如二进制和计数数据。该研究还将解决稳健的HB和EB估计。一般方法将直接适用于前面和后面提到的具体例子。拟议研究的广泛影响是巨大的。开发简单易用的EB置信区间不仅是小范围文献的进步，也是EB方法常规使用的人口统计学，社会学，商业，经济学和保险等领域的广泛问题的进步。这些区间的简单性和数据适应性使它们不仅适用于二进制和计数数据，而且适用于由指数分布和伽马分布拟合的倾斜连续数据。此外，鲁棒HB和EB估计器的构建将为同时估计问题提供一个强大的理论上可行的方法，这些问题再次在不同的研究领域中经常面临。此外，拟议的研究将有助于以研究为基础的研究生培训，使代表性不足的群体参与，并促进机构间和跨学科合作。新的研究成果也将纳入关于调查抽样的研究生课程。该奖项是2006财政年度数学科学优先领域数学社会和行为科学特别竞赛的一部分。

The project will introduce some new empirical and hierarchical Bayesian (EB and HB) methodology which can be used in a wide range of problems in demography, sociology, business, insurance, economics, and surveys. In particular, the methods are expected to be readily applicable to certain small area estimation problems involving both discrete and continuous data. The two major motivating examples for this research are estimation of the proportion of uninsured for minority subpopulations and neighborhood level estimation of the proportion of African-American females suffering from clinical depression. The first topic is of immense relevance to many Federal Agencies such as the Center for Disease Control/National Center for Health Statistics and the United States Bureau of the Census. The second is of direct relevance to researchers engaged in Family and Community Health Study. The project is expected to develop a general class of EB confidence intervals not only for continuous data, but also for discrete data, such as binary and count data. The research will also address robust HB and EB estimation. The general methodology will have direct application to the specific examples mentioned earlier and beyond.The broader impact of the proposed research is enormous. The development of simple and easy to use EB confidence intervals will be an advancement not only for the small area literature, but also for a wide range of problems in demography, sociology, business, economics and insurance where EB methods are routinely used. The simplicity and data-adaptability of these intervals will make them readily usable not only for binary and count data, but also for skewed continuous data fitted by the exponential and gamma distributions. Also, the construction of robust HB and EB estimators will provide a strong theoretically viable method for simultaneous estimation problems, once again routinely faced in diverse research areas. In addition, the proposed research will contribute towards research-based training of graduate students, involve participation of under-represented groups and foster interagency and interdisciplinary collaboration. The new research results also will be incorporated in graduate courses on survey sampling. This award was supported as part of the fiscal year 2006 Mathematical Sciences priority area special competition on Mathematical Social and Behavioral Sciences (MSBS).