A Case Study Competition Among Methods for Analyzing Large Spatial Data

Abstract

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.

References in corpus (8)

• Geometric median and robust estimation in Banach spaces
• Fixed-domain asymptotic properties of tapered maximum likelihood estimators
• Robust and Scalable Bayes via a Median of Subset Posterior Measures
• Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors
• FRK: An R Package for Spatial and Spatio-Temporal Prediction with Large Datasets
• Spectral Density Estimation for Random Fields via Periodic Embeddings
• A Divide-and-Conquer Bayesian Approach to Large-Scale Kriging
• Spatial Mapping with Gaussian Processes and Nonstationary Fourier Features

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• Spectral Density Estimation for Random Fields via Periodic Embeddings
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• Gaussian Markov Random Fields versus Linear Mixed Models for satellite-based PM2.5 assessment: Evidence from the Northeastern USA
• Spatial modelling with R-INLA: A review
• A Linear Mixed Model Formulation for Spatio-Temporal Random Processes with Computational Advances for the Separable and Product-Sum Covariances
• Bayesian Inference for Big Spatial Data Using Non-stationary Spectral Simulation
• Data integration for high-resolution, continental-scale estimation of air pollution concentrations
• Modeling spatial data using local likelihood estimation and a Matérn to SAR translation