Novel Methods for Incorporating Sample Design in Bayesian Inference

这个研究项目将开发方法来解释复杂的样本设计时，使用贝叶斯方法进行统计推断。 社会科学家经常依靠调查来提供有关美国人口的信息。例如，全国健康访谈调查被用来解决与健康有关的问题。研究人员使用这些数据提供基线或人口描述性统计数据，并开发和评估统计模型以预测社会结果。这些统计模型越来越复杂，使得它们非常适合贝叶斯设置，但没有标准方法来解释贝叶斯模型中的样本设计。这个项目将提供一个通用的方法，将复杂的样本设计在贝叶斯推理。 研究人员将把他们的方法整合到通用的IVEware软件中，用于分析调查数据，该软件可在密歇根大学网站上免费向公众提供。他们还将提供一个教育培训的机会，一个有前途的博士生。这个研究项目将建立在调查人员最近开发的方法，将复杂的样本设计在一个加权有限人口贝叶斯自助程序。他们将扩展这种方法，通过重要性加权将设计效果纳入贝叶斯分析。新方法将有非常普遍的应用，该项目将考虑三个具体的应用。该项目将探讨在平均值和方差轨迹的联合纵向数据模型中对复杂样本设计的解释，以使用健康和退休调查从短期记忆测试中预测衰老的开始。在小面积估计方面，该项目将利用国家健康访谈调查和行为风险因素监测调查的数据，对县级风险行为进行估计。 在缺失数据的情况下，该项目将使用来自国家健康和营养检查调查的观察数据，以适应在估算饮食和生物标志物测量时的样本设计和测量误差。

This research project will develop methodology to account for complex sample designs when making statistical inference using Bayesian methods. Social scientists often rely on surveys to provide information about the U.S. population. The National Health Interview Survey, for example, is used to address health-related questions. Researchers use such data to provide baseline or population descriptive statistics and to develop and assess statistical models to predict social outcomes. The increasing complexity of these statistical models makes them well suited to a Bayesian setting, but there is no standard method to account for sample designs in Bayesian models. This project will provide a general approach to incorporate complex sample designs in Bayesian inference. The investigators will incorporate their methods into the general purpose IVEware software for analyzing survey data, which is freely available to the public at the University of Michigan website. They also will provide an educational training opportunity to a promising doctoral student.This research project will build on the methods the investigators recently have developed to incorporate complex sample designs in a weighted finite population Bayesian bootstrap procedure. They will extend this methodology to incorporate design effects into Bayesian analyses via importance weighting. The new methods will have very general application, and the project will consider three specific applications. The project will explore accounting for complex sample design in a joint longitudinal data model of mean and variance trajectories to predict onset of senility from short memory tests using the Health and Retirement Survey. In the setting of small area estimation, the project will develop county-level estimates of risky behavior using a combination of data from the National Health Interview Survey and the Behavioral Risk Factor Surveillance Survey. In a missing data setting, the project will use observed data from the National Health and Nutrition Examination Survey to accommodate both sample design and measurement error when imputing diet and biomarker measures.