Ute Hahn, Eva Jensen, Marie-Colette van Lieshout, Linda Nielsen (Augsburg, Aarhus, CWI, Aarhus)
Locally scaled Markov point processes
Key words: Inhomogeneity, local scaling, sequential spatial processes.
A new class of models for inhomogeneous spatial point processes is introduced. These locally scaled point processes are modifications of homogeneous template point processes, having the property that regions with different intensity differ only by a scale factor, i.e. appear to be scaled versions of the template point process. This is achieved by modifying the conditional intensity or volume measures used in the density according to a scaling function. If the scaling function is constant, then local scaling coincides with global scaling by a constant factor. It is shown that the locally scaled versions are again Markov and that locally the conditional intensity of the new process behaves like that of a global scaling of the homogeneous process.