A review of Markov models for inhomogeneous point processes

Some recent models for inhomogeneous spatial point processes with interaction will be reviewed. The focus is on models derived from homogeneous Markov point processes. For some of the models, the interaction is location dependent. A new type of transformation related model with this property is also suggested. The statistical inference based on likelihood and pseudolikelihood is discussed for the different models. In particular, it is shown that for transformation models, the pseudolikelihood function can be decomposed in a similar fashion as the likelihood function.

Before the review, I will also give a summary of the research at Laboratory for Computational Stochastics.