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A Nonstationary Spatial Covariance Model for Processes Driven by Point Sources

Journal of Agricultural, Biological and Environmental Statistics volume 25, pages 415–430 (2020)Cite this article

Abstract

We introduce a new nonstationary spatial covariance model for analyzing geostatistical point-referenced data that contain point sources (i.e., known locations that impact the outcome). Our model is based on viewing the spatial domain on the polar coordinate scale, with the point source representing the reference location. As a result, we incorporate distances from the point source and angles of the separation vector with respect to the point source into the covariance model definition in order to describe complex correlation patterns that may be induced by the point source. We apply the new model and several competing options to analyze the impact of a hog lot on house sales prices in Cedar Falls, Iowa. We find that the new model offers improved model fit and predictive ability through Watanabe–Akaike information criterion and cross-validation, respectively. Additionally, we design a simulation study to determine the impact that mean misspecification has on each model’s ability to produce quality predictions. Overall, the new model is shown to consistently outperform the competitors and is useful even when the point source has no impact on the outcome.

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Acknowledgements

The author thanks Professor Mark D. Ecker for sharing the hog lot and house sales prices data used in this work.

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  1. Department of Biostatistics, Yale University, New Haven, CT, 06510, USA

    Joshua L. Warren

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  1. Joshua L. Warren
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Correspondence to Joshua L. Warren.

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Warren, J.L. A Nonstationary Spatial Covariance Model for Processes Driven by Point Sources. JABES 25, 415–430 (2020). https://doi.org/10.1007/s13253-020-00404-4

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  • DOI: https://doi.org/10.1007/s13253-020-00404-4

Keywords

  • Bayesian modeling
  • Cross-validation
  • Kriging
  • Polar coordinate system