118 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
Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models
We propose a new class of filtering and smoothing methods for inference in
high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models.
The main idea is to combine the ensemble Kalman filter and smoother, developed
in the geophysics literature, with state-space algorithms from the statistics
literature. Our algorithms address a variety of estimation scenarios, including
on-line and off-line state and parameter estimation. We take a Bayesian
perspective, for which the goal is to generate samples from the joint posterior
distribution of states and parameters. The key benefit of our approach is the
use of ensemble Kalman methods for dimension reduction, which allows inference
for high-dimensional state vectors. We compare our methods to existing ones,
including ensemble Kalman filters, particle filters, and particle MCMC. Using a
real data example of cloud motion and data simulated under a number of
nonlinear and non-Gaussian scenarios, we show that our approaches outperform
these existing methods
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