Hierarchical Bayesian methods for survey sampling and other applications

Abstract

In model-based survey sampling Hierarchical Bayesian (HB) methods have gained immense popularity. One of the major reasons for this popularity remains the convenience in implementation of HB models using MCMC methods even when the models are complex. An inevitable part of this approach is the elicitation of priors for the parameters involved in the model. Authentic expert information can be incorporated by assigning suitable subjective prior distribution to the parameters. In Bayesian analysis nonsubjective or objective priors are assigned to the parameters when reliable subjective information is unavailable. In survey sampling, situations often arise when subjective prior information is unavailable; in such situations noninformative or objective Bayesian methods have great relevance. In this dissertation we study various noninformative HB models which combine information from multiple sources. These models are extensively used in small area estimation. In the first chapter we discuss the outline of the dissertation. In the next two chapters we provide robust small area estimation models which account for possible presence of outliers under two different scenarios. In the fourth chapter we develop robust Bayesian predictors of small area means which account for the possibility when random small area effects are not present for some small areas. In the fifth chapter we develop various HB methods which combine information from different surveys. The methods proposed in this dissertation involve improper priors. We have analytically shown that the posterior distributions based on these priors are proper under mild conditions.