Jump to ContentJump to Main Navigation

Journal of Inverse and III-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

Increased IMPACT FACTOR 2012: 0.560
Mathematical Citation Quotient 2012: 0.50

VolumeIssuePage

Issues

A sensitivity matrix based methodology for inverse problem formulation

A. Cintrón-Arias1 / H. T. Banks2 / A. Capaldi3 / A. L. Lloyd4

1Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

2Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

3Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

4Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 6, Pages 545–564, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.034, August 2009

Publication History:
Received:
2009-04-10
Published Online:
2009-08-19

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

Comments (0)

Please log in or register to comment.
Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.