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Inference in infinite-dimensional inverse problems - Discretization and dualityMany techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.
Document ID
19920072432
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Stark, Philip B.
(California, University Berkeley, United States)
Date Acquired
August 15, 2013
Publication Date
September 10, 1992
Publication Information
Publication: Journal of Geophysical Research
Volume: 97
Issue: B10
ISSN: 0148-0227
Subject Category
Statistics And Probability
Accession Number
92A55056
Funding Number(s)
CONTRACT_GRANT: NAG5-883
CONTRACT_GRANT: NSF DMS-89-57573
CONTRACT_GRANT: NSF DMS-88-10192
CONTRACT_GRANT: NSF DMS-87-05843
Distribution Limits
Public
Copyright
Other

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