Pairwise likelihood methods for inference in image models

We consider parameter estimation for certain random set models for image data. For the spatial models considered here, a full likelihood-based approach to this problem is often difficult, since the likelihood generally cannot be computed for images of typical size. This has motivated the consideration of various less computationally demanding parameter estimation techniques. We discuss one method based on likelihoods for small subsets of the data. Consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of-the basic approach. Results of a simulation study are reported for some variants of the Boolean model and excursion sets of random fields. The methods are illustrated for some data on the spatial incidence of heather.