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A Nonstationary Spatial Covariance Model for Processes Driven by Point Sources

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  • Joshua L. Warren

    (Yale University)

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.

Suggested Citation

  • Joshua L. Warren, 2020. "A Nonstationary Spatial Covariance Model for Processes Driven by Point Sources," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 415-430, September.
    • Handle: RePEc:spr:jagbes:v:25:y:2020:i:3:d:10.1007_s13253-020-00404-4
    DOI: 10.1007/s13253-020-00404-4
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    References listed on IDEAS

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    1. Hughes-Oliver, Jacqueline M. & Gonzalez-Farias, Graciela & Lu, Jye-Chyi & Chen, Di, 1998. "Parametric nonstationary correlation models," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 267-278, October.
    2. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
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    Cited by:

    1. Jiafang Song & Joshua L. Warren, 2022. "A Directionally Varying Change Points Model for Quantifying the Impact of a Point Source," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 46-62, March.

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