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| Titel |
Dimensionality reduction in Bayesian estimation algorithms |
| VerfasserIn |
G. W. Petty |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1867-1381
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| Digitales Dokument |
URL |
| Erschienen |
In: Atmospheric Measurement Techniques ; 6, no. 9 ; Nr. 6, no. 9 (2013-09-04), S.2267-2276 |
| Datensatznummer |
250085054
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| Publikation (Nr.) |
 copernicus.org/amt-6-2267-2013.pdf |
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| Zusammenfassung |
An idealized synthetic database loosely resembling 3-channel passive
microwave observations of precipitation against a variable background
is employed to examine the performance of a conventional Bayesian
retrieval algorithm. For this dataset, algorithm performance is found
to be poor owing to an irreconcilable conflict between the need to
find matches in the dependent database versus the need to exclude
inappropriate matches. It is argued that the likelihood of such
conflicts increases sharply with the dimensionality of the observation
space of real satellite sensors, which may utilize 9 to 13 channels
to retrieve precipitation, for example.
An objective method is described for distilling the relevant
information content from N real channels into a much smaller number (M)
of pseudochannels while also regularizing the background (geophysical
plus instrument) noise component. The pseudochannels are linear
combinations of the original N channels obtained via a two-stage
principal component analysis of the dependent dataset. Bayesian
retrievals based on a single pseudochannel applied to the independent
dataset yield striking improvements in overall performance.
The differences between the conventional Bayesian
retrieval and reduced-dimensional Bayesian retrieval suggest
that a major potential problem with conventional multichannel
retrievals – whether Bayesian or not – lies in the common but
often inappropriate assumption of diagonal error covariance. The
dimensional reduction technique described herein avoids this problem
by, in effect, recasting the retrieval problem in a coordinate system
in which the desired covariance is lower-dimensional, diagonal, and unit magnitude. |
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