Modeling Partially Surveyed Point Process Data: Inferring Spatial Point Intensity of Geomagnetic Anomalies

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 concen...

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Bibliographic Details
Published in:Journal of agricultural, biological, and environmental statistics biological, and environmental statistics, 2020-06, Vol.25 (2), p.186-205
Main Authors: Flagg, Kenneth A., Hoegh, Andrew, Borkowski, John J.
Format: Article
Language:English
Subjects:
Agriculture
Bayesian analysis
Biostatistics
Bombing and gunnery ranges
Computer simulation
Data augmentation
Dirichlet problem
Environmental remediation
Geomagnetism
Health Sciences
Magnetic anomalies
Mathematics and Statistics
Medicine
Military training
Monitoring/Environmental Analysis
Remediation
Spatial data
Statistics
Statistics for Life Sciences
Unexploded ordnance
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Summary: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.
ISSN:1085-7117
1537-2693
DOI:10.1007/s13253-020-00387-2