Alternative to the Autologistic Model Using a Hidden Conditional Autoregressive Gaussian Process

The use of the autologistic model for binary spatial data on a regular lattice is hindered by the necessity to evaluate the normalising constant which is intractable in all but small systems. An alternative Bayesian approach is presented using a hierarchical model where the observed data is the sign of a hidden conditional autoregressive Gaussian process. This has the advantage that the nor-malising constant requires simply evaluating a matrix determinant. Markov chain Monte Carlo simulations are used on real and simulated data to estimate the posterior distribution of the model's spatial dependency parameters .