Intensity-Dependent Point Processes

A practical and theoretically interesting problem in the context of point processes are marked point patterns where the statistical properties of marks depend locally on point intensity. Such dependence can be observed, for example, in fishery data, where catches (marks) are certainly associated with the locations where the fisheries take place (points), in order to optimize capture effort. In intensity-marked point processes, the marks are allowed to be marginally correlated and the mark size depends locally on the point density. In this work, we analyse the relationship between these models and the geostatistical model under preferential sampling. Detecting dependence between marks and locations of marked point processes is an important issue because predictions of the process can be severely biased when standard statistical methodologies are applied to data where the distribution of a mark varies along the point density. The aforementioned relationship was explored in real data.