Autoregressive models for spatial-temporal data

In this dissertation, we focus on statistical modeling of spatial lattice data, which accounts for potential spatial dependence of data on a given lattice and/or temporal dependence over discrete time points. We adopt a Bayesian framework for statistical inference and develop Markov chain Monte Carlo techniques to generate simulations from the posteriors and predict into the future.; The dissertation consists of three parts. The first part concerns the statistical inference of spatial-temporal autologistic regression model (STARM) developed by Zhu et al. (2005) for the analysis of spatial-temporal binary data. We develop a Metropolis-Hastings algorithm combined with either a Gibbs sampler or perfect simulation to obtain the posterior distributions of the model parameters as well as the posterior predictive distributions. We demonstrate the methodology and compare the results with maximum pseudolikelihood and MCMC maximum likelihood approaches via a real data example concerning southern pine beetle outbreak.; The second part concerns statistical modeling and inference of spatial panel data in spatial econometrics. Due to computational difficulties involved in optimization over a high-dimensional parameter space, the existing spatial panel models tend to be overly simplistic. Using cigarette demand data in a spatial panel of US for illustration, we propose a general class of spatial-temporal autoregressive models that account for heterogeneity and dependence both across space and over time. We develop Markov chain Monte Carlo algorithms for model parameter inference and prediction.; The third part concerns statistical inference of the spectral density function of a second-order stationary spatial process. We construct a nonparametric Bernstein polynomial prior for the spectral density function and establish its theoretical validity. To simulate from the posterior distribution of the spectral density function, we develop a Markov chain Monte Carlo algorithm based on Whittle's approximation of the likelihood function. We analyze simulated data for illustration.