# A Case Study Competition Among Methods for Analyzing Large Spatial Data

arXiv: https://arxiv.org/abs/1710.05013 · HTML: https://mlsanity.com/paper/1710.05013/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2017.

## Built on by (most cited first, 30 of 44)

- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods](https://mlsanity.com/paper/2305.04634/) (2023)
- [Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernels](https://mlsanity.com/paper/2205.09070/) (2022)
- [MuyGPs: Scalable Gaussian Process Hyperparameter Estimation Using Local Cross-Validation](https://mlsanity.com/paper/2104.14581/) (2021)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models](https://mlsanity.com/paper/2310.12000/) (2023)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [Faster Kernel Interpolation for Gaussian Processes](https://mlsanity.com/paper/2101.11751/) (2021)
- [Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees](https://mlsanity.com/paper/2210.07893/) (2022)
- [Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization](https://mlsanity.com/paper/2301.13303/) (2023)
- [Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data](https://mlsanity.com/paper/2405.14492/) (2024)
- [Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression](https://mlsanity.com/paper/2109.00046/) (2021)
- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework](https://mlsanity.com/paper/2109.04447/) (2021)
- [Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data](https://mlsanity.com/paper/2208.09978/) (2022)
- [Compactly-supported nonstationary kernels for computing exact Gaussian processes on big data](https://mlsanity.com/paper/2411.05869/) (2024)
- [New Bounds for Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2502.08730/) (2025)
- [Adaptive Resolution for Finite-Rank Gaussian Processes](https://mlsanity.com/paper/2505.24066/) (2025)
- [Bayesian Data Sketching for Varying Coefficient Regression Models](https://mlsanity.com/paper/2506.00270/) (2025)
- [Fast Gaussian Process Approximations for Autocorrelated Data](https://mlsanity.com/paper/2512.02925/) (2025)
- [On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach](https://mlsanity.com/paper/2103.03321/) (2021)
- [Fast Gaussian Process Posterior Mean Prediction via Local Cross Validation and Precomputation](https://mlsanity.com/paper/2205.10879/) (2022)
- [Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models](https://mlsanity.com/paper/2208.06528/) (2022)
- [Light curve completion and forecasting using fast and scalable Gaussian processes (MuyGPs)](https://mlsanity.com/paper/2208.14592/) (2022)
- [Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis](https://mlsanity.com/paper/2305.13879/) (2023)
- [Implementation and Analysis of GPU Algorithms for Vecchia Approximation](https://mlsanity.com/paper/2407.02740/) (2024)
- [Superior Scoring Rules for Probabilistic Evaluation of Single-Label Multi-Class Classification Tasks](https://mlsanity.com/paper/2407.17697/) (2024)
- [Probabilistic Spatiotemporal Modeling of Day-Ahead Wind Power Generation with Input-Warped Gaussian Processes](https://mlsanity.com/paper/2409.16308/) (2024)
- [Correspondence of NNGP Kernel and the Matern Kernel](https://mlsanity.com/paper/2410.08311/) (2024)

## Abstract (arXiv)

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each which was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online.