Analyzing nonstationary spatial data using piecewise Gaussian processes
Analyzing nonstationary spatial data using piecewise Gaussian processes
复制标题
DOI：
10.1198/016214504000002014
复制
发表时间：
2005-06-01
影响因子：
3.7
通讯作者：
Holmes, CC
中科院分区：
文献类型：
--
作者：
Kim, HM;Mallick, BK;Holmes, CC
在地质统计学的许多问题中，感兴趣的响应变量与空间位置的基础地质密切相关。在这种情况下，在不同的岩层中发现的响应往往几乎没有相关性，因此潜在的协方差结构在岩石类型的边界处显示出急剧的变化。传统的平稳和非平稳空间方法是不合适的，因为它们通常假设点之间的协方差是距离的平滑函数。在这篇文章中，我们提出了一种通用的方法，用于分析潜在协方差结构急剧变化的空间数据。我们的方法的工作原理是自动将空间域分解成不相交的区域，在这些区域中，过程被假设为静止的，但数据被假设为跨区域独立的。不相交区域的数量、其形状和区域内模型的不确定性以完全贝叶斯的方式处理。我们在以前未发表的关于德克萨斯州伍德县施耐德·布达油田土壤渗透性的数据集上说明了我们的方法。
In many problems in geostatistics the response variable of interest is strongly related to the underlying geology of the spatial location. In these situations there is often little correlation in the responses found in different rock strata, so the underlying covariance structure shows sharp changes at the boundaries of the rock types. Conventional stationary and nonstationary spatial methods are inappropriate, because they typically assume that the covariance between points is a smooth function of distance. In this article we propose a generic method for the analysis of spatial data with sharp changes in the underlying covariance structure. Our method works by automatically decomposing the spatial domain into disjoint regions within which the process is assumed to be stationary, but the data are assumed independent across regions. Uncertainty in the number of disjoint regions, their shapes, and the model within regions is dealt with in a fully Bayesian fashion. We illustrate our approach on a previously unpublished dataset relating to soil permeability of the Schneider Buda oil field in Wood County, Texas.