Spatial factor modeling: A Bayesian matrix‐normal approach for misaligned data

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...

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Bibliographic Details
Published in:Biometrics Vol. 78; no. 2; pp. 560 - 573
Main Authors: Zhang, Lu, Banerjee, Sudipto
Format: Journal Article
Language:English
Published: United States Blackwell Publishing Ltd 01.06.2022
Subjects:
Algorithms
Bayes Theorem
Bayesian analysis
Bayesian inference
Bayesian theory
Computer applications
Computer Simulation
data collection
Datasets
Dependent variables
factor models
Linear Models
linear models of coregionalization
Mathematical models
mathematical theory
matrix‐normal distribution
Multivariate analysis
multivariate spatial processes
Normal Distribution
Physical sciences
scalable spatial modeling
Spatial data
Statistical analysis
Statistical inference
uncertainty
Variables
Vegetation index
multivariate spatial processes
factor models
Bayesian inference
scalable spatial modeling
matrix-normal distribution
linear models of coregionalization
ISSN:0006-341X, 1541-0420, 1541-0420
Online Access:Get full text
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Summary: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 are the theme of this article, refer 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.
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ISSN:0006-341X
1541-0420
1541-0420
DOI:10.1111/biom.13452