39 research outputs found
A multi-resolution approximation for massive spatial datasets
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.Comment: 23 pages; to be published in Journal of the American Statistical
Associatio
Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition
We propose an approximation to the forward-filter-backward-sampler (FFBS)
algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in
Bayesian statistics when working with linear Gaussian state-space models, but
it requires inverting covariance matrices which have the size of the latent
state vector. The computational burden associated with this operation
effectively prohibits its applications in high-dimensional settings. We propose
a scalable spatio-temporal FFBS approach based on the hierarchical Vecchia
approximation of Gaussian processes, which has been previously successfully
used in spatial statistics. On simulated and real data, our approach
outperformed a low-rank FFBS approximation