# High-dimensional Multivariate Geostatistics: A Bayesian Matrix-Normal Approach

arXiv: https://arxiv.org/abs/2003.10051 · HTML: https://mlsanity.com/paper/2003.10051/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso](https://mlsanity.com/paper/2101.02404/) (2021)
- [Bayesian Classification with Probit-link Split-and-merge Gaussian Process Prior in EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/2605.30775/) (2026)

## Abstract (arXiv)

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This manuscript develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a Vegetation Index data set with spatially dependent observations numbering in the millions.