Determining high-risk zones for unexploded World War Ⅱ bombs by using point process methodology

摘要

To prevent accidents caused by unexploded bombs from the Second World War, high-risk zones need to be determined. We introduce two statistical methods to determine such zones by considering patterns of exploded and unexploded bombs as realizations of inhomo-geneous spatial Poisson point processes. The first method is based on the intensity of the point process; the second method on its nearest neighbour distance. Although the performance of the two methods is similar, the intensity-based method has the advantage of a more direct specification of risk and should hence be preferred. Risk that is associated with a zone is defined as the probability that not all unexploded bombs are in the zone. We propose and develop a procedure to calculate this probability. This procedure is then also used to investigate consequences of additional spatial clustering, in which case the intensity-based method is shown to be conservative. Our work is motivated and illustrated by World War II explosive ordnance disposal by German authorities on the basis of aerial pictures taken by the allies.