Point sources in spatially referenced data can impact outcomes in surrounding locations (e.g., a factory that emits air pollution). Previous statistical methods have sought to describe the non-stationary correlation induced by the presence of a point source, with fewer attempting to quantify its overall impact. We introduce directionally varying change points (DVCP), a model that aims to estimate the magnitude of the impact of a point source as well as its range of influence across the spatial domain. DVCP allows for a unique change point parameter, describing the range of influence of a point source, at every angle extending from the source and uses a Gaussian process with directionally defined correlation function to facilitate estimation of the parameters. The Gaussian predictive process approximation is used for fitting the model to large datasets. Through simulation, we show that DVCP can easily accommodate a wide range of shapes defining the range of influence. We apply DVCP to better understand spatial patterns of ambient PM\(_{2.5}\) concentrations and issues related to environmental inequity in California and Colorado. The method is available in the R package DVCP.

Supplementary materials accompanying this paper appear online.

空间参考数据中的点源会影响周围位置的结果（例如，排放空气污染的工厂）。以前的统计方法试图描述由点源的存在引起的非平稳相关性，很少尝试量化其整体影响。我们引入了定向变化的变化点 (DVCP)，这是一种旨在估计点源影响的大小及其在空间域中的影响范围的模型。DVCP 允许唯一的变化点参数，描述点源在从源延伸的每个角度的影响范围，并使用具有方向定义的相关函数的高斯过程来促进参数的估计。高斯预测过程近似用于将模型拟合到大型数据集。通过模拟，我们表明 DVCP 可以轻松适应定义影响范围的各种形状。我们应用 DVCP 来更好地理解环境 PM 的空间模式\(_{2.5}\)加州和科罗拉多州与环境不公平相关的浓度和问题。该方法在 R 包DVCP 中可用。

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