A spatial model is a random field and only one realization is available and hence point estimation of such models are difficult. Computational intractability of normalizing constant of the joint density is the problem. Maximum pseudo-likelihood etimation (MPLE) is the simplest approach for estimation of the parameters for spatially dependent binary random variables or autologistic model. MPLE (Ref. 1) is based on the pseudo-binary function defined by the product of the conditional distributions by maximizing with respect to the parameters using standard logistic regression estimation techniques. However if the observations are independent then the functions coincide in trivial cases. Hence, MPLEs are consistent and asymptotically normal but not efficient, efficiency being positively related to the value of the spatial dependence parameter. There are two reasons for considering Approximate maximum likelihood estimation (AMLE) as appropriate for autologistic model. First, no likelihood evaluation is necessary and normalizing constant is thus not required. Second, the theory of AMLE is effective when approximate Bayesian computation (ABC) is based on sufficient statistics. For an auto logistic model, sufficient statistics are available. It can be applied to other spatial models as well. (46 refs.)
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