空间协方差结构中空间变化方向效应的解释
Accounting for spatially varying directional effects in spatial covariance structures
摘要：
风向在一个地理区域内污染物水平的传播中起着重要作用。讨论了如何在空间模式的协方差函数中加入风向信息。我们遵循最初由Higdon及其合著者提出的空间卷积方法，其中空间过程由平滑核和白噪声过程之间的卷积描述。我们提出了两种不同的方式占风向的核函数。为了比较的目的，我们还考虑了一个更灵活的内核参数化，它利用了在整个区域内平滑变化的潜在过程。推理过程遵循贝叶斯范式，并且在执行空间插值时自然考虑到关于参数估计的不确定性。我们分析了在美国东北部的一个监测网络中观察到的臭氧水平。与基于潜在过程的核相比，我们提出的模型下的后验分布的样本获得得更快。我们的模型提供了更好的结果，在模型拟合和空间插值方面，相比简单的各向同性和几何各向异性模型。尽管参数的数量很少，我们提出的模型提供了适合的内核下获得的潜在过程的基础上。
英文摘要：
Wind direction plays an important role in the spread of pollutant levels over a geographical region. We discuss how to include wind directional information in the covariance function of spatial models. We follow the spatial convolution approach initially proposed by Higdon and co-authors, wherein a spatial process is described by a convolution between a smoothing kernel and a white noise process. We propose two different ways of accounting for wind direction in the kernel function. For comparison purposes, we also consider a more flexible kernel parametrization, that makes use of latent processes which vary smoothly across the region. Inference procedure follows the Bayesian paradigm, and uncertainty about parameter estimation is naturally accounted for when performing spatial interpolation. We analyze ozone levels observed at a monitoring network in the Northeast of the USA. Sam- ples from the posterior distribution under our proposed models are obtained much faster when compared to the kernel based on latent processes. Our models provide better results, in terms of model fitting and spatial interpolation, when compared to simple isotropic and geometrical anisotropic models. Despite the small number of parameters, our proposed models provide fits which are comparable to those obtained under the kernel based on latent processes.
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