Bayesian Spatial Models for Small Area Estimation;Doctoral thesis

摘要

This work consists of three parts. For the first portion the authors consider a generalized linear model with possible correlated random effects. The authors use a Bayesian hierarchical generalized linear mixed model to estimate success rates at a post-stratified level. The model includes an autoregressive process and spatially correlated random geographic effects. The application is the 1996 Missouri Turkey Hunting Survey. In the second portion the authors incorporate both pre- and post-stratification into a Bayesian hierarchical framework. The authors propose a new family of generalized linear mixed models with correlated random effects when there are two unknown canonical parameters. Such a family can be used to model both random sample sizes and success probabilities in small area estimation under pre-and post-stratification. General formulae for Bayesian estimation and prediction at the post-stratification level are given. One application is the 1998 Missouri Turkey Hunting Survey, which was pre-stratified based on the hunter's place of residence.