LJKProbability & Statistics Seminar

On Thursday September 26 2013 at 14h00 in Salle 1  Tour IRMA

Seminary of Michaela PROKESOVA (Charles University, Prague, RÃ©publique TchÃ¨que)

Spacetime cluster point processes  models and estimation

Summary

In the talk we will discuss a class of parametric models suitable for modeling of clustered spacetime point patterns which are encountered e.g. in epidemiology. Namely we will introduce the shotnoise Cox processes. The model produces clustered point patterns (i.e. there are interactions among the points of the point process) and enables the first 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 refined threestep estimation procedure based on minimum contrast estimation. We discuss asymptotic properties of the introduced estimation procedure and investigate its properties for mediumsized point patterns by a simulation study.
