  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.
