Bayesian Methods for Small Area Estimation and Latent Structure Models

本研究主要集中在贝叶斯方法在具有离散结果的小区域估计中的应用。由于公共和私营部门对小面积估计的需求，小面积估计在调查抽样中变得越来越流行。在小区域估计的典型实例中，仅有个别区域的少数样本可用。因此，直接调查估计值往往具有较大的标准误差和变异系数。合并来自相似邻近地区的信息通常会改善对某个区域平均值的估计，或同时估计几个区域平均值。经验贝叶斯方法和层次贝叶斯方法特别适合于满足这种从相关小领域“借力”的需要。新的估计方法将提供更可靠的估计，并减少标准误差。调查员将应用新方法分析各种社会、医疗和环境数据；例如，调查员将估计按年龄、性别和种族交叉分类的几个当地地区对工作满意的人的百分比。其他可能的应用包括在工作中暴露在危害健康的环境中，估计癌症死亡率，分析存在危险废物场地的死亡率，以及空间数据分析。研究人员研究的另一个方面将集中在潜在结构模型的分层和经验贝叶斯分析上。著名的Rasch车型将作为特例包括在内。这一分析将为社会心理数据的分析提供统一的方法。

The primary focus on this research is on applications of Bayesian methods to small area estimation with discrete outcomes. Small area estimation is becoming increasingly popular in survey sampling owing to the demand for small area estimates from both public and private sectors. In typical instances of small area estimation, only a few samples are available from individual areas. The direct survey estimates, therefore, tend to have large standard errors and coefficients of variation. Incorporating information from similar neighboring areas typically improves an estimate of a certain area mean, or the simultaneous estimation of several area means. Empirical and hierarchical Bayes methods are particularly well-suited to meet this need of `borrowing strength` from related small areas. The new methods of estimation will provide much more reliable estimates with reduced standard errors. The investigator will apply the new methods to the analysis of various social, medical, and environmental data; e.g., the investigator will estimate the percentage of people satisfied with their job in several local areas cross-classified by age, sex, and race. Other possible applications include exposure to health hazards in jobs, estimation of cancer mortality rates, analysis of mortality rates in the presence of hazardous waste sites, and analysis of spatial data. Another aspect of the investigator's research will concentrate on hierarchical and empirical Bayes analysis of latent structure models. The celebrated Rasch model will be included as a special case. This analysis will provide unified method for the analysis of social and psychological data.