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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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Online
ISSN
1569-3945
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In This Section
Volume 17, Issue 6 (Jan 2009)

Issues

A sensitivity matrix based methodology for inverse problem formulation

A. Cintrón-Arias
  • Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:
/ H. T. Banks
  • Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:
/ A. Capaldi
  • Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:
/ A. L. Lloyd
  • Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:
Published Online: 2009-08-19 | DOI: https://doi.org/10.1515/JIIP.2009.034

Abstract

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.

Key words.: Inverse problems; ordinary least squares; sensitivity matrix; Fisher Information matrix; parameter selection; standard errors

About the article

Received: 2009-04-10

Published Online: 2009-08-19

Published in Print: 2009-08-01



Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2009.034. Export Citation

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