Markov chain Monte Carlo for a Spatial-Temporal Autologistic Regression Model

Abstract

An existing spatial-temporal autologistic regression model relates a binary response variable to potential covariates while accounting for both dependence on a spatial lattice and dependence over discrete time points. This approach is useful for analyzing spatial-temporal binary data. However, the existing statistical inference is via maximum pseudo-likelihood and may be statistically inefficient especially when the spatial and temporal dependence is strong. This article proposes a fully Bayesian approach for both model parameter inference and prediction at future time points using Markov chain Monte Carlo (MCMC). A Metropolis–Hastings algorithm combined with a Gibbs sampler or perfect simulation are developed for obtaining the posterior distributions of 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.