Point processes – abstraction and practical relevance

All statistical modelling of complex data structures involves an abstraction to the essential properties of interest into quantifiable units and associated random variables. In addition, it also often goes along with simplifying assumptions as part of the abstraction process, typically for practical reasons. As a result, methodology can tend to be far removed from reality and hence be of little practical relevance.
In the context of point process modelling, the usual abstraction reduces the available information to locations of points in space, whose spatial structure is analysed. Classical simplifications often concern assumptions of homogeneity, isotropy and known detection probabilities, often for computational reasons. Recent computational improvement however, allows us to relax some of these assumptions.
This talk provides a number of examples of how we have been able to relax these classical assumptions along with associated abstractions, leading to increased practical relevance. In particular, I will discuss how this increased practical relevance has also caused an increasing demand for the development of new methodology that has previously played a rather minor role.