Bayesian Analysis of Sample Surveys

抽样调查中的两个关键问题是偏差，这是由于无法接触到目标人口的所有部分（未覆盖）或选定的调查对象未作出答复而造成的，另一个问题是由于抽样规模不足而造成的差异或缺乏准确性。 提高精确度的一种方法是使统计模型与调查答复相适应;然而，实际应用受到无法适应足够灵活的模型的限制。 这项研究的计划是开发模型，将有关调查设计的信息和其他知识，如人口分布的协变量，目前使用的经典加权方法，以减少偏差和方差的抽样调查估计。 这种方法的一个特别关注的问题是考虑到数据收集的设计，并使我们的新方法与现有的基于设计的抽样调查分析方法“向后兼容”。 从统计学的角度来看，要建立一个能反映调查设计中所有特征的模型，需要对预测变量之间具有复杂层次结构的线性和逻辑回归模型进行研究，研究的最终目的是为样本调查推理提供一种常规方法，这种方法将基于模型的推理的灵活性与基于设计的推理的可靠性结合起来。 这项工作将潜在地推进三个领域：统计抽样推断、贝叶斯方法和抽样调查的应用，特别是在社会科学和公共卫生领域。 建模方法允许部分汇集人口中不同结构水平（例如，学校教室和个别学生）之间的估计值，并且对于估计小型亚群和处理由复杂因素组合引起的无应答特别有效。 例如，在民意调查中，研究人员可能对不同人口群体或国家不同地区之间的意见差异感兴趣。 在对儿童的公共卫生调查中，人们可能希望确定高危行为的预测因素。

Two key concerns in sample surveys are bias, caused by inability to reach all sections of the target population (noncoverage) or nonresponse on the part of selected subjects, and variance or lack of precision, caused by inadequate sample sizes. One approach to increase precision is to fit statistical models to the survey response; however, practical application has been limited by an inability to fit sufficiently flexible models. The plan of this research is to develop models that incorporate information about the design of the survey and other knowledge, such as population distributions of covariates, that is currently used in classical weighting methods to reduce the bias and variance of sample survey estimates. A special concern of this approach is to account for the design of the data collection and to make our new methods "backward compatible" with existing design-based analysis methods for sample surveys. Statistically, developing models to account for all the features in a survey design requires research in linear and logistic regression models with complex hierarchical structures among the predictor variables.The research is intended ultimately to yield routine methods for sample survey inference that combine the flexibility of model-based inference with the reliability of design-based inference. This work will potentially advance three areas: statistical sampling inference, Bayesian methods, and the applications of sample surveys, especially in social science and public health. The modeling approach allows the partial pooling of estimates between different structural levels in the population (for instance, school classrooms and individual students), and is particularly effective for estimating small subpopulations and for dealing with nonresponse that is caused by complex combinations of factors. For example, in opinion polls a researcher may be interested in differences in opinion between different demographic groups or different regions of the country. In a public health survey of children, one may wish to identify predictors of high-risk behavior.