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

In a project, commissioned by the North Sea Directorate, Ministry of Transport and Public Works (RWS), the problem is to estimate the intensity of oil pollution in the Dutch part of the North Sea. A planar inhomogeneous Poisson point process with an intensity function, which is parametrized by a finite dimensional parameter, was used as a spatial model for the locations of the centres of the oilspots. The parametrization enables us to incorporate the available a priori knowledge about oil pollution, such as the location of sources of oil pollution (i.e. shipping areas or off-shore locations) and the intensity of shipping in various regions. The distribution of the volumes (marks) of oil spots is completely unknown, but we can use the volumes of the observed oil spots 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), which were supplied by RWS. A relatively simple form of spatial bootstrapping was used in order to estimate the accuracy of the estimated total amount of oil pollution in the North Sea.