Bayesian wombling: Curvilinear gradient assessment under spatial process models
Bayesian wombling: Curvilinear gradient assessment under spatial process models
复制标题
DOI：
10.1198/016214506000000041
复制
发表时间：
2006-12-01
影响因子：
3.7
通讯作者：
Gelfand, Alan E.
中科院分区：
文献类型：
--
作者：
Banerjee, Sudipto;Gelfand, Alan E.
利用空间过程模型对区域上的随机空间表面进行大规模推理已经得到了很好的研究。在这样的模型下，表面的局部分析（例如，在给定点处的梯度）最近受到关注。一个更雄心勃勃的目标是从点移动到曲线，试图为曲线分配有意义的梯度。对于一个点，如果某个方向的梯度很大（正或负），则曲面在该方向上快速增加或减少。对于曲线，如果在与曲线正交的方向上的梯度趋于大，则曲线跟踪通过曲面快速变化的区域的路径。在文献中。了解表面在何处呈现快速变化称为摆动，而我们所描述的曲线称为摆动边界。现有的wombling方法主要集中在识别点，然后连接这些点使用一个特设的算法来创建曲线wombling边界。这种方法不容易纳入统计建模环境。本文的贡献是形式化的概念曲线wombling边界的矢量分析框架，使用参数曲线和开发一个全面的统计框架曲线边界分析的基础上，空间过程模型的点参考数据。对于可以表示自然特征的给定曲线（例如，一座山，一条河，或一个政治边界），我们解决了测试或评估它是否是一个摇摆不定的边界的问题。我们的方法既适用于空间响应曲面，也适用于空间残差曲面（通常更恰当）。我们说明了我们的方法与模拟研究，天气数据集的状态科罗拉多，和物种存在/不存在的数据集从康涅狄格州。
Large-scale inference for random spatial surfaces over a region using spatial process models has been well studied. Under such models, local analysis of the surface (e.g., gradients at given points) has received recent attention. A more ambitious objective is to move from points to curves, to attempt to assign a meaningful gradient to a curve. For a point, if the gradient in a particular direction is large (positive or negative), then the surface is rapidly increasing or decreasing in that direction. For a curve, if the gradients in the direction orthogonal to the curve tend to be large, then the curve tracks a path through the region where the surface is rapidly changing. In the literature. learning about where the surface exhibits rapid change is called wombling, and a curve such as we have described is called a wombling boundary. Existing wombling methods have focused mostly on identifying points and then connecting these points using an ad hoc algorithm to create curvilinear wombling boundaries. Such methods are not easily incorporated into a statistical modeling setting. The contribution of this article is to formalize the notion of a curvilinear wombling boundary in a vector analytic framework using parametric curves and to develop a comprehensive statistical framework for curvilinear boundary analysis based on spatial process models for point-referenced data. For a given curve that may represent a natural feature (e.g., a mountain, a river, or a political boundary), we address the issue of testing or assessing whether it is a wombling boundary. Our approach is applicable to both spatial response surfaces and, often more appropriately, spatial residual surfaces. We illustrate our methodology with a simulation study, a weather dataset for the state of Colorado, and a species presence/absence dataset from Connecticut.