A Multi-Resolution Approximation for Massive Spatial Datasets

ABSTRACT

Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new insights on a wide variety of issues. However, traditional spatial-statistical techniques such as kriging are not computationally feasible for big datasets. We propose a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space. The M-RA process is specified as a linear combination of basis functions at multiple levels of spatial resolution, which can capture spatial structure from very fine to very large scales. The basis functions are automatically chosen to approximate a given covariance function, which can be nonstationary. All computations involving the M-RA, including parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelized to take full advantage of large distributed-memory computing environments. In comparisons using simulated data and a large satellite dataset, the M-RA outperforms a related state-of-the-art method. Supplementary materials for this article are available online.

KEYWORDS:

• Basis functions
• Distributed computing
• Full-scale approximation
• Gaussian process
• Kriging
• Satellite data

Supplementary Materials

All Julia code, R code to produce the plots, and the data for Section 4.2 are available online.

Acknowledgement

The author thanks Dorit Hammerling, Doug Nychka, Mikyoung Jun, Joe Guinness, Huiyan Sang, Suhasini Subba Rao, Valen Johnson, and two anonymous referees for helpful comments and suggestions. The author is also grateful to John Forsythe and Stan Kidder for providing the dataset in Section 4.2 and helpful advice.

Funding

This research was partially supported by NASA's Earth Science Technology Office AIST-14 program and by National Science Foundation (NSF) Grant DMS-1521676.