A COMPARISON OF BAYESIAN MODELS FOR SPATIALLY CORRELATED BINARY LATTICE DATA

Douglas Gorman , Masters Candidate, Department of Statistics, Colorado State University.
ABSTRACT
This paper compares the performance of two Bayesian models commonly used to analyze spatially correlated binary data. The models, described by their prior distributions, are the autologistic and latent Gaussian models. The two approaches are compared for their ability to estimate pixel values for a known, but degraded, twodimensional lattice of correlated binary pixels. Both models employ locally dependent Markov random fields as prior distributions for the true lattice values. The autologistic model incorporates spatial dependence using a spatial autologistic regression model, where the probability of success for a site of interest depends on the values of neighboring sites in the lattice and neighboring sites are assumed to have similar binary responses. The latent Gaussian model is a hierarchical Bayesian model that employs a logistic regression model with a spatially correlated random effect. A Gaussian conditional autoregressive prior is used to model the correlated random effects and thus the binary lattice is assumed to have an underlying continuous distribution in which pixels are correlated.
Parameter estimation proceeds via Markov chain Monte Carlo, specifically Gibbs sampling, for both models. Gibbs sampling is a natural choice for estimation, since the priors are locally dependent Markov random fields which specify the conditional distribution of each pixel (parameter) given the values of the other pixels in the lattice.
The two models are compared using a map of presence/absence data for a species of vegetation over a geographic region. For the scenarios considered here the two models lead to quite different results, though they are comparable in their ability to reconstruct the binary lattice from its degraded state.
