IJPAM: Volume 105, No. 3 (2015)
MODELS ADMITTING MULTIPLE PARAMETRIZATIONS
John Nardini, H.T. Banks, W. Clayton Thompson
Center for Research in Scientific Computation
Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8212, USA
Cardiovascular and Metabolic Diseases Research Unit
Cambridge, MA 02139, USA
Abstract. When estimating parameters using noisy data, uncertainty quantification methods provide a way to investigate the confidence one has in the parameter estimates, as well as to obtain information on the possible dependence of parametric estimators on one another. In this note, we consider uncertainty quantification techniques that allow visualization of the distributions of these parameter estimators for evidence of possible correlation. We consider three mathematical models (the logistic curve, the Richards curve, and the spring equation), which permit multiple parametrizations, and compare the corresponding parameter estimators for possible dependence/independence. The uncertainty quantification techniques we employ include the correlation coefficients, asymptotic as well as exact confidence regions or ellipsoids, and Monte Carlo plots generated by the DRAM algorithm.
Received: October 20, 2015
AMS Subject Classification:
Key Words and Phrases: inverse problems, effects of parameterizations, independent vs. dependent estimators, exact vs. asymptotic confidence ellipsoids, Monte Carlo simulations, Bayesian analysis, DRAM
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DOI: 10.12732/ijpam.v105i3.16 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 497 - 522