Classical kriging models use Euclidean distance when modeling spatial autocorrelation. However for regions with irregular boundaries and holes, such as estuaries and coastlines, a measure of within-domain distance may capture a system’s proximity dependencies more accurately. Standard kriging techniques are not guaranteed to yield a valid covariance structure when defined in terms of non-Euclidean distances. In this paper, we develop a new kriging model for irregularly shaped domains. Our model uses an approximation to a diffusion process to define a valid covariance structure that reflects the domain topology. A covariance matrix is defined through the use of random walks on a lattice, process convolutions, and the kriging equations. A simulation study demonstrates that for commonly encountered topologies, our diffusion kriging estimator is superior to a kriging estimator based on shortest within-domain distance. We also illustrate our method using water quality data from Puget Sound and Lake Peipsi to map chlorophyll concentration.

中文翻译：

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基于随机游走的具有不规则边界和孔洞的克里格区域的地统计模型

经典克里金模型在建模空间自相关时使用欧几里德距离。然而，对于具有不规则边界和洞的区域，例如河口和海岸线，域内距离的测量可以更准确地捕获系统的邻近依赖性。当根据非欧几里得距离定义时，标准克里金技术不能保证产生有效的协方差结构。在本文中，我们针对不规则形状的域开发了一种新的克里金模型。我们的模型使用扩散过程的近似来定义反映域拓扑的有效协方差结构。协方差矩阵是通过使用格子上的随机游走、过程卷积和克里金方程来定义的。模拟研究表明，对于常见的拓扑，我们的扩散克里金估计器优于基于最短域内距离的克里金估计器。我们还使用普吉特海湾和佩普西湖的水质数据来说明我们的方法，以绘制叶绿素浓度图。