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Inverse Problems as Statistics

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Surveys on Solution Methods for Inverse Problems

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Abstract

What mathematicians, scientists, engineers, and statisticians mean by “inverse problem” differs. For a statistician, an inverse problem is an inference or estimation problem. The data are finite in number and contain errors, as they do in classical estimation or inference problems, and the unknown typically is infinite-dimensional, as it is in nonparametric regression. The additional complication in an inverse problem is that the data are only indirectly related to the unknown. Standard statistical concepts, questions, and considerations such as bias, variance, mean-squared error, identifiability, consistency, efficiency, and various forms of optimality apply to inverse problems. This article discusses inverse problems as statistical estimation and inference problems, and points to the literature for a variety of techniques and results.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720-3860, USA

    P. B. Stark

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  1. P. B. Stark
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    David Colton

  2. Institut für Mathematik, Johannes-Kepler-Universität, Linz, Austria

    Heinz W. Engl

  3. Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Federal Republic of Germany

    Alfred K. Louis

  4. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York, USA

    Joyce R. McLaughlin

  5. Department of Mathematics, Texas A & M University, College Station, Texas, USA

    William Rundell

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© 2000 Springer-Verlag/Wien

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Stark, P.B. (2000). Inverse Problems as Statistics. In: Colton, D., Engl, H.W., Louis, A.K., McLaughlin, J.R., Rundell, W. (eds) Surveys on Solution Methods for Inverse Problems. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6296-5_13

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  • DOI: https://doi.org/10.1007/978-3-7091-6296-5_13

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83470-1

  • Online ISBN: 978-3-7091-6296-5

  • eBook Packages: Springer Book Archive

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