Bayesian model checking for generalized linear spatial models for count data
Hierarchical models are increasingly used in many of the earth sciences. A class of Generalized Linear Mixed Models was proposed by Diggle, Tawn and Moyeed (1998) for the analysis of spatial non-Gaussian data, but model estimation, checking and selection in this class of models remain difficult tasks due to the presence of an unobservable latent process. Model checking methods within this class have not been considered so far in the literature. We consider this class of models for the analysis of spatial count data. We implement robust Markov Chain Monte Carlo algorithms with the help of advanced techniques, such as group updating, Langevin-Hastings algorithms, and data-based transformations, for estimation and posterior sampling. Then we investigate the application of model checking methods based on measures of relative predictive surprise, as those described in Bayarri and Castellanos (2007). We also propose and investigate an alternative model checking method to diagnose incompatibility between model and data based on a kind of transformed residuals. The usefulness of the proposed model checking methods is explored using both simulated and real spatial count data, and the results are compared with the results from other Bayesian model checking methods. An R package is developed to implement all the methods discussed in the dissertation by using advanced computing techniques, such as R/C++ interfacing and parallel computing.