Abstract:
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Automated sensing instruments on satellites and aircraft have enabled the collection of big spatial data over large and inhomogenous spatial domains. If these kinds of 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 (i.e., non-gridded) 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 inhomogenous spatial structure from very fine to very large scales. The basis functions are chosen to optimally approximate a given covariance function, and no restrictions on the covariance function are necessary. All computations involving the M-RA, including fully Bayesian parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelized to take full advantage of distributed computing environments.
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