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 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. Electronic Supplementary Material Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.

Computationally efficient joint species distribution modeling of big spatial data

“…The HMSC model augmented with a GPP or a NNGP displayed much better scaling of computational complexity than the originally proposed spatial HMSC, and much better performance than the nonspatial HMSC. We also note that, in addition to the considered GPP and NNGP, there exist other prominent spatial statistical methods (Heaton et al 2018) that could prove useful for spatial JSDMs in the future. However, the superiority of NNGP over GPP may have been favored by some case-specific factors.…”

“…In this study we explore two approaches from spatial statistics that has been shown to enable efficient modeling of big spatial data sets: Gaussian predictive process (GPP; Banerjee et al 2008, Finley et al 2015 and nearestneighbor Gaussian process (NNGP; Datta et al 2016), although we note that various alternative techniques are also available (Heaton et al 2018). This means that the model is practically infeasible to apply to data sets even with moderately large numbers of sites, such as n y being in the order of thousands.…”

Scalable inference for space‐time Gaussian Cox processes

“…A recent ‘contest’ article by Heaton et al . () shows many methods, including the one we adopt here, to be very competitive and delivering effectively indistinguishable inference on the spatial process.…”

“…A comprehensive review is beyond the scope of the current article; see recent review articles by Sun et al (2012) and Banerjee (2017). A recent 'contest' article by Heaton et al (2017) shows many methods, including the one we adopt here, to be very competitive and delivering effectively indistinguishable inference on the spatial process.One approach that is receiving much traction in high-dimensional spatial statistics is based on Vecchia (1988), who proposed a computationally efficient likelihood approximation based on what could be characterized as a directed acyclic graph, or DAG, decomposition of the joint multivariate Gaussian density exploiting a much smaller set of conditional variables determined from nearest neighbors. This idea is now commonly used in graphical Gaussian models to introduce sparsity in the precision matrix.…”

Synthesizing simulation and field data of solar irradiance

“…They continue to show how the method can be applied to a vast set of , massively parallelized when such architectures are available , and how the result takes on a nonstationary flavor where spatial dependence can vary throughout the input domain. Hybrid versions developed by Sun et al , which essentially combine ordinary “global” GPs applied to (computationally manageable) subsets of the data with (full data) laGPs on the residuals, have led to competitive results compared to other publicly available software .…”