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.
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: https://doi.org/10.1515/JIIP.2009.034.
Frequentist and Bayesian Lasso Techniques for Parameter Selection in Nonlinearly Parameterized Models**This research was supported in part by the Department of Energy National Nuclear Security Administration (NNSA) through the Consortium for Nonproliferation Enabling Capabilities (CNEC) award number DE-NA0002576.