Novel Methods for Incorporating Sample Design in Bayesian Inference

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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.