Topics in Bayesian Design and Analysis for Sampling

Yutao Liu

Survey sampling is an old field, but it is changing due to recent advancement in statistics and data science. More specifically, modern statistical techniques have provided us with new tools to solve old problems in potentially better ways, and new problems arise as data with complex and rich information become more available nowadays. This dissertation is consisted of three parts, with the first part being an example of solving an old problem with new tools, the second part solving a new problem in a data-rich setting, and the third part from a design perspective. All three parts deal with modeling survey data and auxiliary information using flexible Bayesian models. In the first part, we consider Bayesian model-based inference for skewed survey data. Skewed data are common in sample surveys. Using probability proportional to size sampling as an example, where the values of a size...