Gaussian process modeling of heterogeneity and discontinuities using Voronoi tessellations

TL;DR

This paper presents a flexible Gaussian process modeling approach for spatial data with heterogeneity and discontinuities, using Voronoi tessellations to partition the space and an adaptive sampling method to identify region borders.

Contribution

It introduces a novel combination of Voronoi tessellations and Gaussian processes for non-stationary spatial modeling, allowing complex region shapes and adaptive border detection.

Findings

Effective in modeling heterogeneous spatial processes.

Capable of handling non-convex and disconnected regions.

Improves border identification with adaptive sampling.

Abstract

Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities. The problem of non-stationarity is dealt with by using a combination of Voronoi tessellation to partition the input space, and a separate Gaussian process to model the data on each region of the partitioned space. Our method is highly flexible because we allow the Voronoi cells to form relationships with each other, which can enable non-convex and disconnected regions to be considered. In such problems, identifying the borders between regions is often of great importance and we propose an adaptive sampling method to gain extra information along such borders. The method is illustrated with simulation studies and application to real data.