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Optimal parameterization of a mathematical model for solving parameter estimation problems

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Abstract:

This article presents a method to solve parameter estimation problems by finding an optimal parameterization of the mathematical model. The pi-theorem of dimensional analysis is used to establish a formulation of the model based on dimensionless products and scaling parameters, together with the rules of a parameterization change. Logarithmic parameters are introduced for the purpose of working in a linear parameter space in which a given base corresponds to a specific parameterization. The optimal parameterization is assumed to yield uncorrelated estimators. A statistical independence criterion based on the Fisher information matrix is derived for maximum-likelihood estimators. The method allows one to solve inverse problems with highly correlated model parameters by identifying well-resolved parameters, leading to a solution expressed in terms of correlation laws between physical quantities.

Keywords: Dimensional analysis; Fisher information; Inverse problems; Logarithmic parameters; Optimal parameterization; Parameter estimation; Regularization

Document Type: Research Article

DOI: https://doi.org/10.1080/10682760412331313405

Publication date: 2005-04-01

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