Assessing goodness of fit of spatially inhomogeneous Poisson processes

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.