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Biometrika 2001 88(2):487-497; doi:10.1093/biomet/88.2.487
© 2001 by Biometrika Trust
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Assessing goodness of fit of spatially inhomogeneous Poisson processes

A.Brix1, R.Senoussi2, P.Couteron3 and J.Chadoeuf4

1 University of Copenhagen, Department of Biostatistics, Blegdamsvej 3, 2200 Copenhagen N, Denmarkanders.brix{at}guycarp.com 2 INRA, Unité de Biométrie, Domaine Saint-Paul, Site Agroparc, 84914 Avignon Cedex 9, France.senoussi{at}avignon.inra.fr 3 Ecole Nationale du Génie Rural des Eaux et Forcts 648, rue J.-F. Breton, B.P. 5093, 34033 Montpellier Cedex 01, France. couteron{at}engref.fr 4 INRA, Unité de Biométrie, Domaine Saint-Paul, Site Agroparc, 84914 Avignon Cedex 9, France. joel{at}avignon.inra.fr

We propose an extension of the classical complete spatial randomness tests to nonstationary Poisson spatial processes.The method consists of first performing the classical tests locally and then grouping the local results into a global test. The global test is a test for nonstationary Poisson process assumption, whereas the local tests can be used in an exploratory way to decide whether the observed process is locally regular or clustered or if we do not reject the inhomogeneous Poisson assumption. Under a Cox assumption, an optimal partition of the sampling window can be derived. Finally, we present some examples from forestry and weed sciences.

Key Words: Complete spatial randomness; Inhomogeneous Poisson point process

Received July 2000. Revised October 2000


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Y. Guan
A goodness-of-fit test for inhomogeneous spatial Poisson processes
Biometrika, December 1, 2008; 95(4): 831 - 845.
[Abstract] [PDF]


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