Spatial Factor Modeling: A Bayesian Matrix-Normal Approach for Misaligned Data

TL;DR

This paper introduces a Bayesian matrix-normal based method for scalable multivariate spatial modeling, effectively handling high-dimensional data with improved inference and computational efficiency.

Contribution

It extends scalable univariate spatial models to multivariate processes using matrix-normal distributions, enabling efficient Bayesian inference for high-dimensional data.

Findings

Demonstrates computational efficiency over existing methods.

Provides accurate uncertainty quantification for latent spatial processes.

Successfully analyzes a large vegetation index dataset.

Abstract

Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for each variable and associations among the different dependent variables. Multivariate latent spatial process models have proved effective in driving statistical inference and rendering better predictive inference at arbitrary locations for the spatial process. High-dimensional multivariate spatial data, which is the theme of this article, refers to data sets where the number of spatial locations and the number of spatially dependent variables is very large. The field has witnessed substantial developments in scalable models for univariate spatial processes, but such methods for multivariate spatial processes, especially when the number of outcomes are moderately large, are limited in comparison. Here, we extend scalable modeling strategies for a single process to multivariate processes. We pursue Bayesian inference which is attractive for full uncertainty quantification of the latent spatial process. Our approach exploits distribution theory for the Matrix-Normal distribution, which we use to construct scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliver inference over a high-dimensional parameter space including the latent spatial process. We illustrate the computational and inferential benefits of our algorithms over competing methods using simulation studies and an analysis of a massive vegetation index data set.