Space-time cluster point processes - models and estimation

In the talk we will discuss a class of parametric models suitable for modeling of clustered space-time point patterns which are encountered e.g. in epidemiology. Namely we will introduce the shot-noise Cox processes. The model produces clustered point patterns (i.e. there are interactions among the points of the point process) and enables the first order intensity function (i.e. the mean number of points occurring in different locations of the observation window) to be inhomogeneous and dependent on covariates.
Since the maximum likelihood estimation is computationally prohibitive in this case, some other moment method must be used for parameter estimation. Moreover the high flexibility of the model brings along quite high dimensionality of the parameter space and the necessity of a large enough amount of data for reasonably stable estimation. That is why we introduce a suitable partial separability assumption (the whole model is not separable) which enables to use the spatial and temporal projection processes for estimation. The possible problem of two much overlapping of the clusters in the temporal projection process is addressed by a refined three-step estimation procedure based on minimum contrast estimation. We discuss asymptotic properties of the introduced estimation procedure and investigate its properties for medium-sized point patterns by a simulation study.