Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as \emph{wombling} boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States.
翻译:空间过程模型被广泛用来模拟不同科学领域产生的点参照变量。分析由此产生的随机表面可以更深刻地洞察研究反应中潜在依赖性的性质。我们开发贝叶斯模型和推论,以快速改变反应表面,评估特定轨道的方向曲线。这种快速变化的轨迹或曲线,通常称为emph{wombling}边界,以洪水平原、道路、山区或高原的河流或导致反应地表高梯度的其他地形特征的形式出现在地理空间中。我们展示了完全基于Bayesian方向曲线的推断模型,以分析子宫边界沿线反应中的差异行为。我们用若干模拟实验方法来说明我们的方法,然后以波士顿住房数据为主的多种应用; 使用河流数据;以及来自美国东北部的温度数据。