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Global structure of sloppiness in a nonlinear model
Author(s) -
Tafintseva Valeria,
Tøndel Kristin,
Ponosov Arcady,
Martens Harald
Publication year - 2014
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2651
Subject(s) - nonlinear system , series (stratigraphy) , subspace topology , mathematics , principal component analysis , set (abstract data type) , multivariate statistics , algorithm , computer science , statistics , mathematical analysis , paleontology , biology , programming language , physics , quantum mechanics
The problem of structural ambiguity or “sloppiness” of a mathematical model is here studied by multivariate metamodeling techniques. If a given model is “sloppy”, it means that a number of different parameter combinations—“a neutral parameter set”—can give more or less the same model behavior and thus equally good fit to data. This paper presents a way to characterize the structure of such sloppiness. The model used for illustration is a nonlinear dynamic model of reaction kinetics—a simple version of the S‐system model. When fitted to time series data by various nonlinear curve fitting methods, an unexpected problem was discovered: For every time series, a large neutral parameter set was observed. Each of these sets was analyzed by principal component analysis and found to have clear, but nonlinear, subspace structure. The neutral parameter sets were found for many different time series data, and the global sloppiness structure of the model was characterized. This global sloppiness structure of the model allowed us to find strong correlations between parameters, and on this basis to simplify the original model. A method to reduce the ambiguity in kinetic model parameter estimates based on combining several time series is suggested. Copyright © 2014 John Wiley & Sons, Ltd.