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

该项目将引入一些新的经验和分层贝叶斯(EB和HB)方法，可用于人口学、社会学、商业、保险、经济学和调查的广泛问题。特别是，这些方法有望很容易地适用于某些既涉及离散数据又涉及连续数据的小区域估计问题。这项研究的两个主要激励例子是对少数族裔亚群未参保比例的估计和对患有临床抑郁症的非裔美国女性比例的估计。第一个专题与疾病控制中心/国家卫生统计中心和美国人口普查局等许多联邦机构密切相关。第二个是与从事家庭和社区健康研究的研究人员直接相关的。该项目预计将不仅为连续数据，而且也为离散数据，如二进制和计数数据，开发一类通用的EB置信度区间。这项研究还将解决稳健的HB和EB估计问题。一般方法将直接应用于前面和前面提到的具体例子。拟议研究的更广泛影响是巨大的。发展简单易用的EB可信区间不仅是对小区域文献的进步，也是对人口学、社会学、商业、经济学和保险学中经常使用EB方法的广泛问题的进步。这些区间的简单性和数据适应性将使它们不仅容易用于二进制和计数数据，而且还可以用于指数分布和伽马分布拟合的倾斜连续数据。此外，稳健的HB和EB估计量的构造将为同时估计问题提供一个强大的理论上可行的方法，这在不同的研究领域中再次面临。此外，拟议的研究将有助于研究生的研究性培训，让代表性不足的群体参与，并促进机构间和学科间的合作。新的研究成果也将被纳入有关调查抽样的研究生课程。该奖项作为2006财政年度数学科学优先领域数学社会科学和行为科学特别竞赛的一部分得到支持。

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).