Regularization of statistical inverse problems and the Bakushinskii veto
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Date
2010
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Volume
1564
Issue
Journal
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WIAS Preprints
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract
Literaturverz. In the deterministic context Bakushinskiui's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskiui's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical inverse problems and perform a systematic clarification of the key ideas of statistical regularization
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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.