Statistics Surveys

A comparison of spatial predictors when datasets could be very large

Jonathan R. Bradley, Noel Cressie, and Tao Shi

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In this article, we review and compare a number of methods of spatial prediction, where each method is viewed as an algorithm that processes spatial data. To demonstrate the breadth of available choices, we consider both traditional and more-recently-introduced spatial predictors. Specifically, in our exposition we review: traditional stationary kriging, smoothing splines, negative-exponential distance-weighting, fixed rank kriging, modified predictive processes, a stochastic partial differential equation approach, and lattice kriging. This comparison is meant to provide a service to practitioners wishing to decide between spatial predictors. Hence, we provide technical material for the unfamiliar, which includes the definition and motivation for each (deterministic and stochastic) spatial predictor. We use a benchmark dataset of $\mathrm{CO}_{2}$ data from NASA’s AIRS instrument to address computational efficiencies that include CPU time and memory usage. Furthermore, the predictive performance of each spatial predictor is assessed empirically using a hold-out subset of the AIRS data.

Article information

Statist. Surv., Volume 10 (2016), 100-131.

Received: October 2014
First available in Project Euclid: 19 July 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H11: Directional data; spatial statistics
Secondary: 62P12: Applications to environmental and related topics

Best linear unbiased predictor GIS massive data reduced rank statistical models model selection


Bradley, Jonathan R.; Cressie, Noel; Shi, Tao. A comparison of spatial predictors when datasets could be very large. Statist. Surv. 10 (2016), 100--131. doi:10.1214/16-SS115.

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