The dashed area is the Dutch part of the continental shelf in the North
Sea. The tiny triangles represent the locations of off-shore activities
and the shaded areas correspond to the various shipping areas and also indicate
the different shipping intensities in these areas.
Oil spots are observed by a surveillance aircraft with varying frequencies at different locations. A planar inhomogeneous Poisson point process with intensity function - parametrized by a finite dimensional parameter - is used as a spatial (parametric) model for the locations of (the centres of) oil spots. The parametrization by the parameter vector enables one to incorporate the available a priori knowledge about oil pollution, such as the location of sources of oil pollution and the various shipping intensities. However, not much seems to be known about the distribution of the volumes of oil spots, but we can of course use the sizes of the observed oil spots to estimate it (nonparametric approach).
In this setup a simple semiparametric form of spatial bootstrapping was developed. The idea is to simulate many (a few thousands) realizations of an inhomogeneous planar Poisson process with estimated (from the real data at hand) intensity , where is an estimate of . In addition, we also resample the observed spot volumes in an appropriate manner. With the aid of these resampled datasets, we can obtain accurate bootstrap based confidence limits for the total amount of oil pollution in a given period of time (e.g. the year 1993).
This work is part of CWI's research programme Mathematics & the Environment.