Modeling Non-Stationary Processes Through Dimension Expansion

TL;DR

This paper introduces a novel dimension expansion method to transform nonstationary spatial fields into stationary ones by embedding them into higher-dimensional spaces, improving modeling of complex spatial processes.

Contribution

The paper presents a new approach combining multi-dimensional scaling, group lasso, and latent variables to effectively model nonstationary spatial fields through dimension expansion.

Findings

Dimension expansion successfully models nonstationary fields in simulations.

Application to UK air pollution data demonstrates practical utility.

Method outperforms traditional nonstationary modeling approaches.

Abstract

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.