Bayesian Modeling with Spatial Curvature Processes

Abstract

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 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. Supplementary materials for this article are available online.

KEYWORD:

• Bayesian modeling
• Directional curvature
• Gaussian processes
• Wombling

Supplementary Materials

The online supplement includes additional theoretical derivations and computational details on spatial curvature processes, additional simulation experiment results referenced in Section V D and wombling for Northeastern US temperatures during January, 2000.

Acknowledgments

The authors thank the Editor, Associate Editor, and two anonymous reviewers for several helpful comments that improved the manuscript.

Additional information

Funding

Sudipto Banerjee was supported, in part, by the National Science Foundation (NSF) through grants DMS-2113778 and DMS-1916349; and by the National Institute of Environmental Health Sciences (NIEHS) under grants R01ES030210 and R01ES027027