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.

中文翻译：

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点源驱动过程的非平稳空间协方差模型

我们引入了一种新的非平稳空间协方差模型，用于分析包含点源（即影响结果的已知位置）的地统计点参考数据。我们的模型基于在极坐标尺度上查看空间域，点源代表参考位置。因此，我们将点源的距离和分离向量相对于点源的角度合并到协方差模型定义中，以描述可能由点源引起的复杂相关模式。我们应用新模型和几个相互竞争的选项来分析猪场对爱荷华州锡达福尔斯的房屋销售价格的影响。我们发现新模型通过 Watanabe-Akaike 信息准则和交叉验证提供了改进的模型拟合和预测能力，分别。此外，我们设计了一项模拟研究，以确定均值错误指定对每个模型产生质量预测的能力的影响。总体而言，新模型的表现始终优于竞争对手，即使在点源对结果没有影响的情况下也很有用。