Statistical methods for spatial screening

Abstract

<p>Military bases that have been used for weapon-testing and training usually are contaminated with unexploded ordnance (UXO). These sites can be returned to public use only after UXO remediation. The cleaning-up procedure is usually very expensive and time-consuming. This demands statistical tools to provide more effective sampling strategy and to characterize the UXO distribution. Based on the physical characteristics of UXO deposition, we adopt a simplified Neyman-Scott process to model the UXO distribution. A line transect survey is used to collect data on one coordinate of individual object locations. Two-stage (global and local) sampling strategy is applied to screen the contaminated site. In the global sampling, the estimators of the cluster intensity, mean cluster size and cluster dispersion are provided. The theoretical variance estimators of all the cluster parameters are also given. Simulation studies show that all the parameter estimates perform well and their theoretical variance estimates are reasonably close to their corresponding sample variances. In the local sampling, an inclusion region for covering all the unobserved objects in a cluster is proposed. Its asymptotic coverage property is given and proved. Simulation studies show the actual coverage of the inclusion region is very close to the nominal level.</p>