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Title: Spatial cluster point processes with marks depending on clusters Authors:  Ute Hahn - University of Aarhus (Denmark) [presenting]
Abstract: Cluster processes are obtained as the superposition of finite point processes, the daughters, centred in the points of a parent process. We will introduce and discuss a model where the daughter processes are marked point processes, with i.i.d. ground process, but with mark distribution that is different for different clusters and has relatively narrow bounded support. The overall mark distribution is then a mixture of the cluster mark distributions; therefore the marked cluster process is also clustered in mark space. For this model, it can be shown that the pair correlation function of the parent process can be retrieved, up to a convolution, from the pair correlation function and the mark correlation function of the cluster process. The motivation comes from a data set regarding ultra microscopy, where points represent localizations of single molecules. The points are obtained from fluorescence photons that are registered in a video, and thus they are equipped with time marks. Usually, these data sets are only analysed as point processes in space, but the extra information given by the time marks provides interesting insight into the generation of the data.