Title

A Sensitivity Matrix Methodology for Inverse Problem Formulation

Authors

Ariel Cintron-Arias, East Tennessee State University
H. T. Banks, North Carolina State University at Raleigh
Alex Capaldi, Valparaiso UniversityFollow
Alun L. Lloyd, North Carolina State University at Raleigh

Document Type

Article

Publication Date

8-1-2009

Journal Title

Journal of Inverse and Ill-Posed Problems

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.

Comments

DOI: 10.1515/JIIP.2009.034 (from http://www.degruyter.com/view/j/jiip.2009.17.issue-6/jiip.2009.034/jiip.2009.034.xml)

Recommended Citation

Ariel Cintron-Arias, H. T. Banks, Alex Capaldi, and Alun L. Lloyd. "A Sensitivity Matrix Methodology for Inverse Problem Formulation" Journal of Inverse and Ill-Posed Problems 17.6 (2009): 545-564.