Bayesian Analysis of Sample Surveys

抽样调查中的两个关键问题是偏差，这是由于无法覆盖目标人群的所有部分(未覆盖)或选定对象没有回答，以及由于样本量不足造成的差异或缺乏精确度。提高精度的一种方法是将统计模型与调查答复相适应；然而，由于无法适应足够灵活的模型，实际应用受到了限制。这项研究的计划是开发包含有关调查设计的信息和其他知识的模型，例如协变量的总体分布，这些知识目前在经典加权方法中使用，以减少抽样调查估计的偏差和方差。这种方法的一个特别关注点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”。从统计学上讲，要建立模型来考虑调查设计中的所有特征，需要研究预测变量之间具有复杂层次结构的线性和Logistic回归模型。这项研究的最终目的是给出常规的抽样调查推理方法，将基于模型的推理的灵活性和基于设计的推理的可靠性结合起来。这项工作可能会推进三个领域：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方面。建模方法允许在总体的不同结构水平(例如，学校教室和个别学生)之间部分汇集估计，并且对于估计小的亚群和处理由复杂的因素组合引起的无反应特别有效。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观点差异感兴趣。在对儿童的公共健康调查中，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.