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

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 Matérn 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).

References in corpus (9)

• Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models
• Cross-Covariance Functions for Multivariate Geostatistics
• A general framework for Vecchia approximations of Gaussian processes
• Permutation and Grouping Methods for Sharpening Gaussian Process Approximations
• Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains
• Spatial Factor Modeling: A Bayesian Matrix-Normal Approach for Misaligned Data
• High-dimensional Multivariate Geostatistics: A Bayesian Matrix-Normal Approach
• Spatial Multivariate Trees for Big Data Bayesian Regression
• Spatial meshing for general Bayesian multivariate models