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

Area of Science:

• Environmental science
• Physical science
• Spatial statistics

Background:

• Multivariate spatial data are common in environmental and physical sciences.
• Jointly modeling multiple variables at spatial locations is crucial for understanding associations.
• Existing scalable models are limited for high-dimensional multivariate spatial processes.

Purpose of the Study:

• To extend scalable modeling strategies to multivariate spatial processes.
• To develop Bayesian inference methods for high-dimensional multivariate spatial data.
• To enable better statistical and predictive inference for complex spatial datasets.

Main Methods:

• Utilized distribution theory for the matrix-normal distribution.
• Constructed scalable versions of hierarchical linear model of coregionalization (LMC) and spatial factor models.
• Employed Bayesian inference for full uncertainty quantification of latent spatial processes.

Main Results:

• Developed computationally efficient and statistically robust algorithms for high-dimensional multivariate spatial data.
• Demonstrated improved inference over competing methods through simulation studies.
• Successfully analyzed a large-scale vegetation index dataset.

Conclusions:

• The proposed scalable Bayesian models effectively handle high-dimensional multivariate spatial data.
• The methods offer significant computational and inferential advantages.
• This work advances the analysis of complex spatial processes in environmental and physical sciences.