Linear inference and underparameterized models

Details Linear inference and underparameterized models Linear inference and underparameterized models

Nov 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977rvgsp..15..446p&link_type=abstract

Reviews of Geophysics and Space Physics, vol. 15, Nov. 1977, p. 446-456.

Physics

Geophysics

15

Geophysics, Linear Systems, Parameterization, Statistical Analysis, Data Smoothing, Fourier Series, Hilbert Space, Mathematical Models, Matrices (Mathematics)

Scientific paper

The paper describes the development of a version of Backus's theory of linear inference by use of a new finite-dimensional space. This approach provides a 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 which differs from Backus's treatment. The new approach is analyzed, and it is concluded 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 considered.

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