Inference in infinite-dimensional inverse problems: Discretization and duality

Details Inference in infinite-dimensional inverse problems: Discretization and duality Inference in infinite-dimensional inverse problems: Discretization and duality

Sep 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jgr....9714055s&link_type=abstract

Journal of Geophysical Research, Volume 97, Issue B10, p. 14055-14082

Statistics

Computation

19

General Or Miscellaneous: Techniques Applicable In Three Or More Fields, Seismology: Core And Mantle, Seismology: Instruments And Techniques, Geomagnetism And Paleomagnetism: Instruments And Techniques

Scientific paper

Many 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.

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