Statistics for Locally Scaled Point Processes
Recently, locally scaled point processes have been proposed as a new class of models for inhomogeneous spatial point processes. They are obtained as modifications of homogeneous template point processes and have the property that regions with different intensity differ only by a location dependent scale factor. The main emphasis of the present paper is on analysis of such models. Statistical methods are developed for estimation of scaling function and template parameters as well as for model validation. The proposed methods are assessed by simulation and used in the analysis of a vegetation pattern.
Key wordsInhomogeneous spatial point processes Local scaling of point processes Model validation and simulation
Unable to display preview. Download preview PDF.
- P. Armstrong. Species patterning in heath vegetation of the Northern Sandplain. Honours Thesis, Murdoch University, Western Australia, 1991.Google Scholar
- A.J. Baddeley, M. Hazelton, J. Møller and R. Turner. Residuals and diagnostics for spatial point processes. Abstract, 54 ISI Session Berlin, 13–20 August, 2003.Google Scholar
- O.E. Barndorff-Nielsen. Information and Exponential Families in Statistical Theory. Wiley, Chichester, 1978.Google Scholar
- P.J. Diggle. Statistical Analysis of Spatial Point Patterns. Edward Arnold, London, 2003.Google Scholar
- M.N.M. van Lieshout. Markov Point Processes and their Applications. London: Imperial College Press, 2000.Google Scholar
- J. Møller, and R.P. Waagepetersen. Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC, Boca Raton, 2003.Google Scholar
- L.S. Nielsen. Point process models allowing for interaction and inhomogeneity. PhD Thesis, Department of Mathematical Sciences, University od Aarhus, 2001.Google Scholar