Methods for constructing high-risk zones, which can be used in situations where a spatial point pattern has been observed incompletely, are introduced and evaluated with regard to unexploded bombs in federal properties in Germany.

Unexploded bombs from the Second World War represent a serious problem in Germany. It is desirable to search high-risk zones for unexploded bombs, but this causes high costs, so the search is usually restricted to carefully selected areas. If suitable aerial pictures of the area in question exist, statistical methods can be used to determine such zones by considering patterns of exploded bombs as realisations of spatial point processes. The patterns analysed in this thesis were provided by Oberfinanzdirektion Niedersachsen, which supports the removal of unexploded ordnance in federal properties in Germany. They were derived from aerial pictures taken by the Allies during and after World War II.

The main task consists of finding as small regions as possible containing as many unexploded bombs as possible. In this thesis, an approach based on the intensity function of the process is introduced: The high-risk zones consist of those parts of the observation window where the estimated intensity is largest, i.e. the estimated intensity function exceeds a cut-off value c. The cut-off value can be derived from the risk associated with the high-risk zone. This risk is defined as the probability that there are unexploded bombs outside the zone.

A competing approach for determining high-risk zones consists in using the union of discs around all exploded bombs as high-risk zone. The radius is chosen as a high quantile of the nearest-neighbour distance of the point pattern. In an evaluation procedure, both methods yield comparably good results, but the theoretical properties of the intensity-based high-risk zones are considerably better.

A further goal is to perform a risk assessment of the investigated area by estimating the probability that there are unexploded bombs outside the high-risk zone. This is especially important as the estimation of the intensity function is a crucial issue for the intensity-based method, so the risk cannot be determined exactly in advance. A procedure to calculate the risk is introduced. By using a bootstrap correction, it is possible to decide on acceptable risks and find the optimal, i.e. smallest, high-risk zone for a fixed probability that not all unexploded bombs are located inside the high-risk zone.

The consequences of clustering are investigated in a sensitivity analysis by exploiting the procedure for calculating the risk. Furthermore, different types of models which account for clustering are fitted to the data, classical cluster models as well as a mixture of bivariate normal distributions.