# Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework

arXiv: https://arxiv.org/abs/2109.04447 · HTML: https://mlsanity.com/paper/2109.04447/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 66 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Vecchia approximations of Gaussian-process predictions](https://mlsanity.com/paper/1805.03309/) (2018)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice](https://mlsanity.com/paper/1402.4281/) (2014)
- [ExaGeoStat: A High Performance Unified Software for Geostatistics on Manycore Systems](https://mlsanity.com/paper/1708.02835/) (2017)
- [Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments](https://mlsanity.com/paper/1802.00495/) (2018)
- [High-Dimensional Bayesian Geostatistics](https://mlsanity.com/paper/1705.07265/) (2017)
- [spBayes for large univariate and multivariate point-referenced spatio-temporal data models](https://mlsanity.com/paper/1310.8192/) (2013)
- [Hierarchical low rank approximation of likelihoods for large spatial datasets](https://mlsanity.com/paper/1605.08898/) (2016)
- [A Fused Gaussian Process Model for Very Large Spatial Data](https://mlsanity.com/paper/1702.08797/) (2017)

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

- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifolds](https://mlsanity.com/paper/2309.10918/) (2023)

## Abstract (arXiv)

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.