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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Bibliography

1

H.S. Abdel-Khalik, Y. Bang, and C. Wang.
Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis.
Annals of Nuclear Engineering, 52:28-46, 2013.

2

H.T. Banks, R. Baraldi, J. Catenacci, and N. Myers.
Parameter estimation using unidentified individual data in individual based models.
Center for Research in Scientific Computation Technical Report CRSC-TR16-04, NC State University, Raleigh, NC, 2016.

3

H.T. Banks, W.J. Browning, J. Catenacci, and T.E. Wood.
Analysis of a quasi-chemical kinetic food chemistry model.
Center for Research in Scientific Computation Technical Report CRSC-TR16-05, NC State University, Raleigh, NC, 2016.

4

H.T. Banks, S. Hu, and W.C. Thompson.
Modeling and Inverse Problems in the Presence of Uncertainty.
Taylor/Francis-Chapman/Hall-CRC Press, Boca Raton, FL, 2014.

5

P.G. Constantine, E. Dow, and Q. Wang.
Active subspace methods in theory and practice: applications to kriging surfaces.
SIAM Journal on Scientific Computing, 36(4):A1500-A1524, 2014.

6

M. Davidian.
Nonlinear models for univariate and multivariate response.
https://www4.stat.ncsu.edu/davidian/courses.html, 2007.

7

M. Davidian and D. Giltinan.
Nonlinear models for repeated measurement data: An overview and update.
Journal of Agricultural, Biological, and Environmental Statistics, 8:387-419, 2003.

8

C.J. Doona, F.E. Feeherry, and E.W. Ross.
A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing.
International Journal of Food Microbiology, 100(1):21-32, 2005.

9

C.J. Doona, F.E. Feeherry, E.W. Ross, and K. Kustin.
Inactivation kinetics of listeria monocytogenes by high-pressure processing: Pressure and temperature variation.
Journal of Food Science, 77(8):M458-M465, 2012.

10

B.L. Lund, H.E. Berntsen, and B.A. Foss.
Methods for parameter ranking in nonlinear, mechanistic models.
In IFAC World Congress, Prague. Citeseer, 2005.

11

E.W. Ross, I.A. Taub, C.J. Doona, F.E. Feeherry, and K. Kustin.
The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.
International Journal of Food Microbiology, 99(2):157-171, 2005.

12

V. Serment-Moreno, G. Barbosa-Cánovas, J.A. Torres, and J. Welti-Chanes.
High-pressure processing: kinetic models for microbial and enzyme inactivation.
Food Engineering Reviews, 6(3):56-88, 2014.

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DOI: 10.12732/ijpam.v109i4.19 How to cite this paper?

Source: 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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This work is licensed under the Creative Commons Attribution International License (CC BY).

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