Bayesian modeling with spatial curvature processes

TL;DR

This paper introduces a Bayesian approach to analyze rapid changes and directional curvature in spatial response surfaces, enhancing understanding of geographic features like rivers and mountains.

Contribution

It develops a novel Bayesian modeling framework for directional curvature processes to identify and analyze boundaries of rapid change in spatial data.

Findings

Successfully applied to simulated data

Effectively identified boundaries in real geographic datasets

Provided insights into spatial dependence and topographic features

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 \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.