IJPAM: Volume 109, No. 4 (2016)


H.T. Banks$^1$, W.J. Browning$^2$, J. Catenacci$^3$, T.E. Wood$^4$
$^{1,3}$Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC 27695-8212, USA
$^{3,4}$Applied Mathematics, Inc.
Gales Ferry, CT 06335-0637, USA

Abstract. We analyze a quasi-chemical model for bacterial growth in the context of a parameter estimation problem using available experimental data sets. For many of the data sets the dynamics are simple and we show that the quasi-chemical model (QCM) is over parameterized in these cases. This results in larger uncertainty in the estimated parameters and is some cases instability in the inverse problem. We illustrate methods for reducing the uncertainty present in the estimated model parameters. We first consider a model reduction technique where subsets of the QCM parameters are fixed at nominal values and hypothesis testing is used to compare the nested models. An orthogonal decomposition of the sensitivity matrix is used to guide the choice of which parameters are fixed. Additionally, surrogate models are developed to compare to the QCM. In most cases one of the surrogate models is able to fit the data nearly as well as the QCM model while reducing the uncertainty in the model parameters.

Received: July 12, 2016

Revised: August 1, 2016

Published: October 9, 2016

AMS Subject Classification:

Key Words and Phrases: quasi-chemical model, parameter estimation, inverse problem, parameter reduction, parameter ranking, uncertainty quantification
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DOI: 10.12732/ijpam.v109i4.19 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 993 - 1014

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