Halder Aritra, Banerjee Sudipto, Dey Dipak K
Department of Biostatistics, Drexel University, Philadelphia, PA, USA.
Department of Biostatistics, University of California, Los Angeles, CA, USA.
J Am Stat Assoc. 2024;119(546):1155-1167. doi: 10.1080/01621459.2023.2177166. Epub 2023 Mar 8.
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 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.
空间过程模型广泛应用于对源自不同科学领域的点参照变量进行建模。分析由此产生的随机曲面能更深入地洞察所研究响应中潜在依赖性的本质。我们开发了贝叶斯建模和推理方法，用于评估响应曲面上沿给定轨迹的方向曲率的快速变化。这种快速变化的轨迹或曲线，通常称为边界，在地理空间中以洪泛平原中的河流、道路、山脉或高原等地形特征的形式出现，这些特征会导致响应曲面上出现高梯度。我们展示了基于完全模型的贝叶斯推理在方向曲率过程中的应用，以分析沿摆动边界的响应中的差异行为。我们通过一些模拟实验，随后以波士顿住房数据、默兹河数据以及美国东北部的温度数据为特色的多个应用案例来说明我们的方法。
