Spatio‐temporal Modelling of Weeds by Shot‐noise G Cox processes

Tractable space‐time point processes models are needed in various fields. For example in weed science for gaining biological knowledge, for prediction of weed development in order to optimize local treatments with herbicides or in epidemiology for prediction of the risk of a disease. Motivated by the spatio‐temporal point patterns for two weed species, we propose a spatio‐temporal Cox model with intensity based on gamma random fields. The model is an extension of Neyman–Scott and shot‐noise Cox processes to the space‐time domain and it allows spatial and temporal inhomogeneity. We use the weed example to give a first intuitive interpretation of the model and then show how the model is constructed more rigorously and how to estimate the parameters. The weed data are analysed using the proposed model, and both spatially and temporally the model shows a good fit to the data using classical goodness‐of‐fit tests.