Goodness-of-fit for point process models?

A set of locations in time and space is a point pattern: earthquake epicenters, burglaries, animal habitats. The arrangement of these points is generated by a combination of deterministic and stochastic processes. To adequately model data generated by such mechanisms, it is key that a framework is developed to correctly account for both the spatial and the temporal dependencies. Models that incorporate random fields are fast becoming the preferred tool of choice. These allow us to account for inherent variations and spatial dependencies without demanding knowledge of the generating mechanisms. However, we currently lack appropriate measure of fit for these models. This project will look at goodness-of-fit for a range of point process models, using simulation based approaches to better understand how different cross validation regimes affects inference. No familiarity with point processes statistics is needed; however, strong R programming skills are required and familiarity with C++ would be advantageous. Good grades in STATS310 and STATS330 would also be beneficial.