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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Vydané v:	Biometrics Ročník 78; číslo 2; s. 560 - 573
Hlavní autori:	Zhang, Lu, Banerjee, Sudipto
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Blackwell Publishing Ltd 01.06.2022
Predmet:	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
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Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0006-341X 1541-0420 1541-0420
DOI:	10.1111/biom.13452