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.