A multi-resolution approximation for massive spatial datasets

TL;DR

This paper introduces a multi-resolution approximation method for Gaussian processes that efficiently handles massive, irregularly observed spatial datasets, enabling scalable inference and prediction on large-scale satellite data.

Contribution

It proposes a novel multi-resolution basis function approach that captures spatial structure at multiple scales and is computationally scalable for massive datasets.

Findings

Outperforms existing methods on simulated data

Efficiently processes large satellite datasets

Supports parallel computation for scalability

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.