Bayesian Nonstationary Spatial Modeling for Very Large Datasets

TL;DR

This paper introduces a scalable Bayesian nonstationary spatial modeling approach that combines low-rank and tapered components, allowing for efficient analysis of large, heterogeneous spatial datasets with improved accuracy.

Contribution

It proposes a novel nonstationary Bayesian spatial model with flexible basis functions and a combined low-rank and tapered structure for large datasets.

Findings

Model outperforms existing methods on simulated data.

Real-world soil data analysis shows significant improvement.

Extensions increase model flexibility and accuracy.

Abstract

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large spatial domains. Statistical analyses of such datasets provide two main challenges: First, traditional spatial-statistical techniques are often unable to handle large numbers of observations in a computationally feasible way. Second, for large and heterogeneous spatial domains, it is often not appropriate to assume that a process of interest is stationary over the entire domain. We address the first challenge by using a model combining a low-rank component, which allows for flexible modeling of medium-to-long-range dependence via a set of spatial basis functions, with a tapered remainder component, which allows for modeling of local dependence using a compactly supported covariance function. Addressing the second challenge, we propose two extensions to this model that result in increased flexibility: First, the model is parameterized based on a nonstationary Matern covariance, where the parameters vary smoothly across space. Second, in our fully Bayesian model, all components and parameters are considered random, including the number, locations, and shapes of the basis functions used in the low-rank component. Using simulated data and a real-world dataset of high-resolution soil measurements, we show that both extensions can result in substantial improvements over the current state-of-the-art.