A motivating example for this paper is to study a topsoil geochemical process across a large region. In regional environmental health studies, ambient levels of toxic substances in topsoil are commonly used as surrogates for personal exposure to toxic substances. However, toxicity levels in topsoil are usually sparsely measured at a limited number of point locations. Consequently, topsoil measurements only provide highly localized regional information and cannot be representative of the surrounding area. Instead, it is standard practice to use point-referenced measurements of stream sediments, because they are widely available across a region and are correlated with topsoil measurements at nearby locations. For more effective regional modeling of topsoil geochemistry, we develop a spatially varying coefficient model that integrates point-level topsoil and point-referenced area-level stream sediment data. The proposed model incorporates two spatial characteristics: the local spatial autocorrelation in the latent topsoil process and the spatially varying relationship between the latent topsoil and stream sediment processes. The former is modeled indirectly via a conditional autoregressive model for the stream sediment process, and the latter is modeled by spatially varying coefficients that follow a multivariate Gaussian process. We apply the proposed model to a real dataset of arsenic concentration and demonstrate better performance than competing models.

中文翻译：

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表土地球化学区域分析的多尺度空间变化系数模型

本文的一个激励示例是研究一个大区域的表土地球化学过程。在区域环境健康研究中，表土中有毒物质的环境水平通常用作个人接触有毒物质的替代物。然而，表土中的毒性水平通常在有限数量的点位置进行稀疏测量。因此，表土测量只能提供高度局部化的区域信息，不能代表周边地区。相反，标准做法是使用河流沉积物的点参考测量，因为它们在一个地区广泛可用，并且与附近位置的表土测量相关。为了更有效地对表土地球化学进行区域建模，我们开发了一个空间变化系数模型，该模型整合了点级表土和点参考区域级河流沉积物数据。所提出的模型包含两个空间特征：潜在表土过程中的局部空间自相关以及潜在表土和河流沉积过程之间的空间变化关系。前者通过河流沉积过程的条件自回归模型间接建模，后者通过遵循多元高斯过程的空间变化系数建模。我们将所提出的模型应用于砷浓度的真实数据集，并表现出比竞争模型更好的性能。潜在表土过程中的局部空间自相关以及潜在表土和河流沉积过程之间的空间变化关系。前者通过河流沉积过程的条件自回归模型间接建模，后者通过遵循多元高斯过程的空间变化系数建模。我们将所提出的模型应用于砷浓度的真实数据集，并表现出比竞争模型更好的性能。潜在表土过程中的局部空间自相关以及潜在表土和河流沉积过程之间的空间变化关系。前者通过河流沉积过程的条件自回归模型间接建模，后者通过遵循多元高斯过程的空间变化系数建模。我们将所提出的模型应用于砷浓度的真实数据集，并表现出比竞争模型更好的性能。