Gridding and Parameter Expansion for Scalable Latent Gaussian Models of Spatial Multivariate Data

TL;DR

This paper introduces gridding and parameter expansion techniques to enhance the efficiency of MCMC algorithms for large-scale spatial Gaussian process models, enabling scalable analysis of massive spatial datasets.

Contribution

It proposes novel gridding and parameter expansion methods that improve MCMC performance for scalable spatial Gaussian models with big data, addressing covariance estimation issues.

Findings

Enhanced MCMC efficiency in big data spatial models

Effective application to forestry remote sensing data

Improved covariance parameter estimation in synthetic datasets

Abstract

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms for posterior sampling of the latent process, but these may exhibit pathological behavior in estimating covariance parameters. In this article, we introduce gridding and parameter expansion methods to improve the practical performance of MCMC algorithms in terms of effective sample size per unit time (ESS/s). Gridding is a model-based strategy that reduces the number of expensive operations necessary during MCMC on irregularly spaced data. Parameter expansion reduces dependence in posterior samples in spatial regression for high resolution data. These two strategies lead to computational gains in the big data settings on which we focus. We consider popular constructions of univariate spatial processes based on Mat\'ern covariance functions and multivariate coregionalization models for Gaussian outcomes in extensive analyses of synthetic datasets comparing with alternative methods. We demonstrate effectiveness of our proposed methods in a forestry application using remotely sensed data from NASA's Goddard LiDAR, Hyper-Spectral, and Thermal imager (G-LiHT).