Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation

We propose a two-stage algorithm for computing maximum likelihood estimates for a class of spatial models. The algorithm combines Markov chain Monte C arlo methods such as the Metropolis-Hastings-Green algorithm and the Gibbs sampler, and stochastic approximation methods such as the off-line average and adaptive search direction. A new criterion is built into the algorithm so stopping is automatic once the desired precision has been set. Simulatio n studies and applications to some real data sets have been conducted with three spatial models. We compared the algorithm proposed with a direct appl ication of the classical Robbins-Monro algorithm using Wiebe's wheat data a nd found that our procedure is at least 15 times faster.