HR: 1340h
AN: H13A-0401    [Abstracts]
TI: Refined Estimate of Total Variation Enables a More Accurate Parameter and Uncertainty Estimation, as Well as a new Model Selection Procedure
AU: * de Brauwere, A
EM: adebrauw@vub.ac.be
AF: Vrije Universiteit Brussel Department of Analytical and Environmental Chemistry, Pleinlaan 2, Brussels, 1050 Belgium
AU: De Ridder, F
EM: federid@pop.vub.ac.be
AF: Vrije Universiteit Brussel Department of Electricity and Instrumentation, Pleinlaan 2, Brussels, 1050 Belgium
AU: Elskens, M
EM: melskens@vub.ac.be
AF: Vrije Universiteit Brussel Department of Analytical and Environmental Chemistry, Pleinlaan 2, Brussels, 1050 Belgium
AU: Schoukens, J
EM: johan.schoukens@vub.ac.be
AF: Vrije Universiteit Brussel Department of Electricity and Instrumentation, Pleinlaan 2, Brussels, 1050 Belgium
AU: Pintelon, R
EM: rik.pintelon@vub.ac.be
AF: Vrije Universiteit Brussel Department of Electricity and Instrumentation, Pleinlaan 2, Brussels, 1050 Belgium
AU: Baeyens, W
EM: wbaeyens@vub.ac.be
AF: Vrije Universiteit Brussel Department of Analytical and Environmental Chemistry, Pleinlaan 2, Brussels, 1050 Belgium
AB: In almost every field of science and engineering nonlinear equations are increasingly used to model experimental measurements. In this context, we address the problem of accurately estimating the model parameters and their uncertainty. For that, it is essential to correctly take into account the stochastic measurement uncertainties. For instance, if the measurements are subject to individual errors, the parameters are often estimated using a Weighted Least Squares (WLS) method. For estimating the parameter uncertainties, a linearized expression for the covariance matrix exists. Yet, both methods generally assume that the errors on the independent variable(s), also called "input", are negligible, which is often not true in reality. We propose a refinement of the abovementioned parameter and uncertainty estimation methods, which generalises their applicability to cases where input noise is not negligible. An advantage of this method is that the input noise is transformed into output noise, which allows to keep the traditional WLS formalism (and software). The refined methods are evaluated and compared to the original procedures. The results reveal an improved consistency of the refined WLS estimator compared to the original one. An additional advantage of the refined WLS cost function is that its residual value can be interpreted as a sample from a chi square distribution. This property is useful because it enables an internal quality control of the results. In addition, this property allows an objective procedure to select the most appropriate model for describing the data under study, when several competing models are available. The parameter uncertainty estimation is also clearly improved by applying the refined method. By neglecting the effect of the input noise, a (potentially) important origin of the parameter variation is simply ignored. Therefore, without the refinement, the parameter uncertainties are systematically underestimated. Using the refined method, this systematic error disappears.
DE: 4845 Nutrients and nutrient cycling
DE: 4855 Plankton
DE: 4255 Numerical modeling
DE: 3260 Inverse theory
DE: 1615 Biogeochemical processes (4805)
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting