| This dissertation concerns statistical modeling of spatial data with spatial dependency. Many spatial modeling techniques have been developed within a Bayesian hierarchical modeling framework, because it, accommodates more flexible and complex structures of models. The advances in computation, especially Markov chain Monte Carlo algorithms allow implementation of more complex Bayesian methods. The dissertation consists of three parts. The first part focuses on spatial generalized linear mixed models (GLMMs), which provide a general framework for modeling univariate spatial data that are spatially correlated but not necessarily Gaussian. Bayesian hierarchical modeling is used for inference for spatial GLMMs. We also examine various frequentist properties of Bayesian inferences for spatial GLMM and we present a real data example of mountain pine beetle outbreak.;The second part is on statistical modeling and inference for multinomial spatial areal data. We develop a spatial multinomnial model with spatial random effects and model spatial effects by various multivariate CAR, (NMCAR) models. We compare various forms of MCAR models and illustrate them using both simulated and real data examples.;The last part concerns Bayesian disease clustering methods. A Spatial scan approach is one of the most popular cluster detection methods, which uses likelihood ratio tests based on the null hypothesis of no clusters. Bayesian clustering method is an alternative to overcome several limitations of the scan statistics; however it is computationally intensive. We develop possible ways to improve the efficiency of a Bayesian method. |
