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Linear inference and underparameterized models

Linear inference and underparameterized models A version of Backus's theory of linear inference is developed by using a new finite‐dimensional space. This approach affords a clear geometric interpretation of the essential role played by a priori model smoothing assumptions and also facilitates the construction of a theory for the treatment of random data errors that is quite different from the treatment of Backus. When the unknown parameters form a (necessarily incomplete) description of the model, it is possible to formulate a special smoothing assumption that is particularly appropriate; in practical examples this strategy often leads to tighter bounds on the model uncertainty than those obtained with previous assumptions. An analysis of the numerical aspects of the problem forces one to the conclusion that the theory is not competitive numerically with conventional least squares parameter estimation, unless one of the large submatrices in the problem possesses a simple inverse. An example of this kind is discussed briefly. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reviews of Geophysics Wiley

Linear inference and underparameterized models

Reviews of Geophysics , Volume 15 (4) – Nov 1, 1977

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References (16)

Publisher
Wiley
Copyright
Copyright © 1977 by the American Geophysical Union.
ISSN
8755-1209
eISSN
1944-9208
DOI
10.1029/RG015i004p00446
Publisher site
See Article on Publisher Site

Abstract

A version of Backus's theory of linear inference is developed by using a new finite‐dimensional space. This approach affords a clear geometric interpretation of the essential role played by a priori model smoothing assumptions and also facilitates the construction of a theory for the treatment of random data errors that is quite different from the treatment of Backus. When the unknown parameters form a (necessarily incomplete) description of the model, it is possible to formulate a special smoothing assumption that is particularly appropriate; in practical examples this strategy often leads to tighter bounds on the model uncertainty than those obtained with previous assumptions. An analysis of the numerical aspects of the problem forces one to the conclusion that the theory is not competitive numerically with conventional least squares parameter estimation, unless one of the large submatrices in the problem possesses a simple inverse. An example of this kind is discussed briefly.

Journal

Reviews of GeophysicsWiley

Published: Nov 1, 1977

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