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应用于建模来自不同科学领域的点参考变量。分析由此产生的随机曲面能够深入理解所研究响应中潜在依赖关系的本质。我们针对响应曲面上的快速变化发展了贝叶斯建模与推断方法，以评估给定轨迹上的方向曲率。这种快速变化的轨迹或曲线通常被称为"轮廓边界"，在空间地理中表现为洪泛平原上的河流、道路、山脉或高原等地形特征，这些特征会导致响应曲面上的高梯度。我们展示了基于完整模型的贝叶斯推断在方向曲率过程中的应用，以分析沿轮廓边界响应的差异行为。我们通过一系列模拟实验及多个实际应用案例（包括波士顿房价数据、默兹河数据以及美国东北部温度数据）来验证所提出的方法。