Area-interaction point processes

Disentangling mark/point interaction in marked-point processes

In many spatial situations, not only do the point locations of mark variables (e.g. tree heights) play a key role in the underlying process generating mechanism, but there can be interdependence between the marks and points themselves. Although Monte Carlo frequency-domain analyses can separate mark and point structure, theoretical advances for marks have so far related to the conditional mark ...

Nonparametric Estimation of Interaction Functions of Pairwise Interaction Point Processes

The new problem of nonparametric estimation of the interaction function of pairwise interaction point processes is addressed. We rst generalize some limit theorems of Saunders and Funk. Then we propose a very simple nonparametric estimation method based on the generalization. Several examples are shown to illustrate its eecacy.

Perfect Simulation for the Area-interaction Point Process

New space/time interaction tests for spatiotemporal point processes

We propose a new test for space-time interaction, using a Mercer kernel-based statistic for measuring the distance between probability distributions. As a concrete example, using a geocoded, time-stamped dataset from Chicago of almost 9 million calls to 911 between 2007 and 2010, we ask whether any of these call types are associated with shootings or homicides nearby in space and time. Standard...

Nonparametric estimation of interaction functions for two-type pairwise interaction point processes

Nonparametric estimation of interaction functions for twotype pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point process converge to the means of an inhomo...