  In many applications involving spatial point patterns, we find evidence of
inhibition or repulsion. The most commonly used class of models for such
settings are the Gibbs point processes. A recent alternative, at least to the
statistical community, is the determinantal point process. Here, we examine
model fitting and inference for both of these classes of processes in a
Bayesian framework. While usual MCMC model fitting can be available, the
algorithms are complex and are not always well behaved. We propose using
approximate Bayesian computation (ABC) for such fitting. This approach becomes
attractive because, though likelihoods are very challenging to work with for
these processes, generation of realizations given parameter values is
relatively straightforward. As a result, the ABC fitting approach is
well-suited for these models. In addition, such simulation makes them
well-suited for posterior predictive inference as well as for model assessment.
We provide details for all of the above along with some simulation
investigation and an illustrative analysis of a point pattern of tree data
exhibiting repulsion. R-code and datasets are included in the supplementary
material.
