On estimating the intensity of oil-pollution in the North Sea

A detailed description is given of a reliable statistical method for estimating the spatial variation and the amount of oil pollution in the Dutch part of the North Sea. The method described is a planar inhomogeneous Poisson point process with an intensity function, which is parameterized by a finite dimensional parameter, and was used as a spatial model for the locations of the centers of oil spots. The parameterization enables the user to incorporate the available a priori knowledge about oil pollution, such as the location of sources of oil pollution (i.e. shipping areas or offshore locations) and the intensity of shipping in various regions. Although, the distribution of the volumes (marks) of oil spots is completely unknowm, use of the volumes of the observed oil spots can be made to estimate it (non parametric approach). Several estimators for the total amount of oil pollution are proposed and applied to the real data sets (marked planar point patterns). A relatively simple form of spatial boot-strapping was used in order to estimate the accuracy of the estimated total amount of oil pollution in the North Sea.