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：空间过程模型广泛应用于来自不同科学领域的点参考变量建模。分析生成的随机曲面有助于深入理解所研究响应中潜在依赖关系的本质。我们开发了针对响应曲面快速变化的贝叶斯建模与推断方法，以评估沿给定轨迹的方向曲率。这类快速变化的轨迹或曲线（常被称为“wombling”边界）以洪泛平原中的河流、道路、山脉、高原或其他地形特征的形式出现在地理空间中，导致响应曲面产生高梯度。我们展示了基于完全模型的贝叶斯方向曲率过程推断，用于分析沿wombling边界响应的差异行为。我们通过多项模拟实验对该方法进行验证，并进一步应用于波士顿房价数据、默兹河数据以及美国东北部温度数据等多个案例。