Bayesian analysis of cross-classified spatial-temporal data with autocorrelation

This study is focused on the development and application of statistical methods for the analysis of categorical data collected on a regular lattice over space and time. The question of interest is how to test the dependence of two categorical variables with both spatial and temporal autocorrelations.;Autologistic models developed by previous authors to analyze two binary variables collected over space are extended by considering time as one more spatial dimension. We discuss the anisotropy caused by the introduction of time in the models and show how to make inferences for the unknown parameters by using Bayesian posterior distributions. Markov chain Monte Carlo techniques via a Metropolis algorithm are used to generate simulations of the posteriors and a Gibbs Sampler technique is used to approximate a complex normalizing factor of the likelihood.;Reversible jump MCMC methods are adopted for Bayesian model selection and hypothesis testings. Issues related to missing values and irregularity in time are also addressed. Survival models with spatial-temporal autocorrelation are derived from the full autologistic model conditioned on the survival property. Simulation studies are performed for all models and a real dataset is examined to illustrate this method. The overall approach is checked to evaluate the quality of our approximation methodology including the normalizing constant, convergence of MCMC chains and coverage percentage of the true parameters by posterior intervals.