Investigating and Extending Bayesian Methods for Small Area Estimation

描述（由申请人提供）：研究人员通常希望根据当地人口样本的数据来描述小区域的特征，但是，虽然基于随机样本的平均值已知可以提供无偏估计，但当样本很小时，估计值的方差可能相当大。在使用已公布的人口普查数据（如普查区数据）以及许多大规模健康调查时都会出现这个问题。该项目评估小面积估计的贝叶斯模型的性能，特别侧重于它们对人口普查提供的人口数据的性能。该项目利用了一个新来源的可用性：1880年和1940年人口普查的100%人口数据，其中人们在城市中的位置可以进行地理编码。这使得可以从人口中任意抽取多个样本，并将这些样本的小面积估计值与实际人口值进行比较。相同的方法可以应用于低密度郊区和非中心城市县的ED的非地理编码数据。该方法在其他三个主要方面具有创新性。首先，SAE模型性能的大多数评估集中在面积平均值和比例估计值的偏倚和方差上。该项目涉及另一个对空间人口统计学家非常重要的问题：跨地区差异（用于评估空间不平等和居住隔离）。其次，认识到大多数当代大规模调查，包括人口普查使用样本权重来代表复杂的调查设计和纠正模式的单位无响应，我们专门评估的方法，将样本权重的分层贝叶斯框架。在单元级空间贝叶斯模型中，样本权重的使用知之甚少。该项目将研究并进一步开发一种新的空间模型扩展，以处理样本权重。第三，1940年对芝加哥的估计将利用1930年统计区一级的数据，在时间和空间上都依赖于这两个因素。在比较不同模型的结果时，我们将研究一系列情景，不同的样本比例以及小地区的人口规模和地理规模，估计平均值和比例，比较不同样本设计的效果，并评估利用多个指标的贡献。这项工作的结果将包括调查人员的指导方针， 在不同的设计方案下使用适当的统计方法。

DESCRIPTION (provided by applicant): Researchers often wish to characterize small areas based on data from a sample of the local population, but while average values based on random samples are known to provide unbiased estimates, the variance of estimates can be quite large when samples are small. This problem arises in the use of published census data (such as for census tracts) as well as for many large-scale health-related surveys. This project evaluates the performance of Bayesian models for small area estimation with a particular focus on their performance with population data of the type provided by the census. The project exploits the availability of a new source: 100% population data from the Censuses of 1880 and 1940 where people's locations within cities can be geocoded. This allows multiple samples to be drawn at will from the population, and for small area estimates from these samples to be compared with the actual population values. The same methods can be applied with non-geocoded data for EDs in low density suburbs and for non-central city counties. The approach is innovative in three other major ways. First, most assessments of SAE model performance focus on the bias and variance in estimates of area means and proportions. The project deals with another concern that is substantively important to spatial demographers: the variance across areas (which is used to assess spatial inequality and residential segregation). Second, recognizing that most contemporary large scale surveys including the census use sample weights to represent complex survey designs and correct for patterns of unit non-response, we specifically assess methods to incorporate sample weights in the hierarchical Bayesian framework. Little is known about use of sample weights in unit-level spatial Bayesian models. This project will examine and further develop a new extension of spatial models to deal with sample weights. Third, the 1940 estimates for Chicago will draw on both dependence in both time and space, using data at the Enumeration District level in 1930. In comparing results from different models we will examine a range of scenarios, varying sample proportions and the population size and geographic scale of small areas, estimating both means and proportions, comparing the effects of different sample designs, and assessing the contribution of drawing on multiple indicators. The result of this work will include guidelines for investigators for the most appropriate statistical method to use under the different design scenarios.