Bayesian inference for high-dimensional nonstationary Gaussian processes

TL;DR

This paper introduces a Bayesian inference methodology for nonstationary Gaussian processes that is practical for small to moderate datasets, implemented in an accessible R package, enabling better uncertainty quantification in spatial analysis.

Contribution

The paper presents a new Bayesian inference approach for nonstationary GPs applicable to moderately sized data, with implementation in a user-friendly R package.

Findings

Effective Bayesian inference for nonstationary GPs demonstrated on real datasets.

Comparison shows advantages over existing methods in accuracy and computational feasibility.

Software implementation available for practitioners and researchers.

Abstract

In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets on a personal laptop. For statisticians and data scientists who wish to learn about spatially-referenced data and conduct posterior inference and prediction with appropriate uncertainty quantification, the lack of such approaches and corresponding software is a significant limitation. In this paper, we develop methodology for implementing formal Bayesian inference for a general class of nonstationary GPs. Our novel approach uses pre-existing frameworks for characterizing nonstationarity in a new way that is applicable for small to moderately sized data sets via modern GP likelihood approximations. Posterior sampling is implemented using flexible MCMC methods, with nonstationary posterior prediction conducted as a post-processing step. We demonstrate our novel methods on two data sets, ranging from several hundred to several thousand locations, and compare our methodology with related statistical methods that provide off-the-shelf software. All of our methods are implemented in the freely available BayesNSGP software package for R.