Pairwise likelihood methods for inference in image models
David J. Nott and Tobias Rydén
Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998
ISSN 02811944
ISRN LUTFD2/TFMS3145SE

Abstract:

We consider parameter estimation for certain random set and random field
models for image data. For the spatial models considered here, a full likelihood
based approach to this problem is often difficult, since the likelihood typically
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 discussed by
Diggle (1981).


Key words:

pairwise likelihood, random field, random set, estimating equation, image
modelling, excursion set, Boolean model