Multi-resolution (wavelet) based non-stationary covariance modeling
for incomplete data using EM algorithm
Tomoko Matsuo, GSP post doc
Wavelets are versatile multi-resolution bases to
characterize the stochastic features of a non-stationary
(inhomogeneous) spatial field. A method of multi-resolution
based non-stationary covariance, which takes advantage of
the computational efficiency of the discrete wavelet transform,
is augmented to handle the irregularly distributed incomplete
observational data that is often encountered in the Earth sciences
applications.
Using the sparse structure of wavelet coefficients' covariance
or decay properties of wavelet coefficients' correlation within-
and across-scales, the wavelet based covariance can be parameterized
with parsimonious number of hyper-parameters. Additionally,
Expectation Maximization (EM) algorithm can be used to estimate
these hyper-parameters from irregular and incomplete observational data.
The nonstationary spatial structure of environmental
pollutants is being studied using the method, based
on ground-level ozone measurements monitored at 513
stations located in the eastern United States.
*(in colloaboration with D. W. Nychka, and D. Paul)
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