Abstract
Many former military training sites contain unexploded ordnance (UXO) and require environmental remediation. For the first phase of UXO remediation, locations of geomagnetic anomalies are recorded over a subregion of the study area to infer the spatial intensity of anomalies and identify high concentration areas. The data resulting from this sampling process contain locations of anomalies across narrow regions that are surveyed; however, the surveyed regions only constitute a small proportion of the entire study area. Existing methods for analysis require selecting a window size to transform the partially surveyed point pattern to a point-referenced dataset. To model the partially surveyed point pattern and infer intensity of anomalies at unsurveyed regions, we propose a Bayesian spatial Poisson process model with a Dirichlet process mixture as the inhomogeneous intensity function. A data augmentation step is used to impute anomalies in unsurveyed locations and reconstruct clusters of anomalies that span surveyed and unsurveyed regions. To verify that data augmentation reconstructs the underlying structure of the data, we demonstrate fitting the model to simulated data, using both the full study area and two different sampled subregions. Finally, we fit the model to data collected at the Victorville Precision Bombing range in southern California to estimate the intensity surface in anomalies per acre.
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Acknowledgements
Our many thanks go to John Hathaway for providing the Victorville Precision Bombing Range data. We also thank Megan Higgs for her guidance and mentorship throughout the research process, and for reviewing drafts of this manuscript with her fine attention to detail. Finally, we thank Kate Catlett and Neptune & Company, Inc., for asking tough questions about UXO remediation and providing for the application. This research topic would not have come to our attention were it not for Neptune striving for the highest possible standards of statistical rigor in their work.
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Flagg, K.A., Hoegh, A. & Borkowski, J.J. Modeling Partially Surveyed Point Process Data: Inferring Spatial Point Intensity of Geomagnetic Anomalies. JABES 25, 186–205 (2020). https://doi.org/10.1007/s13253-020-00387-2
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DOI: https://doi.org/10.1007/s13253-020-00387-2