Bayesian Spatiotemporal Wombling

TL;DR

This paper introduces a Bayesian framework for identifying and analyzing regions of rapid change in spatiotemporal data surfaces, extending traditional wombling methods to complex surfaces over time.

Contribution

It develops a fully model-based inferential approach for spatiotemporal wombling using geometry and triangulated surface approximations, applicable across various scientific fields.

Findings

Effective in simulation experiments

Successfully applied to environmental and climate data

Provides detailed boundary analysis in brain imaging

Abstract

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed continuously over time) at arbitrary space-time coordinates, scientific interest often turns to gleaning information regarding zones of rapid spatial-temporal change. We develop Bayesian modeling and inference for directional rates of change along a given surface. These surfaces, which demarcate regions of rapid change, are referred to as ``wombling'' surface boundaries. Existing methods for studying such changes have often been associated with curves and are not easily extendable to surfaces resulting from curves evolving over time. Our current contribution devises a fully model-based inferential framework for analyzing differential behavior in spatiotemporal responses by formalizing the notion of a ``wombling'' surface boundary using conventional multi-linear vector analytic frameworks and geometry followed by posterior predictive computations using triangulated surface approximations. We illustrate our methodology with comprehensive simulation experiments followed by multiple applications in environmental and climate science; pollutant analysis in environmental health; and brain imaging.