Parameter Estimation in the Age of Degeneracy and Unidentifiability
| العنوان: | Parameter Estimation in the Age of Degeneracy and Unidentifiability |
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| المؤلفون: | Horacio G. Rotstein, Raghav Patel, Dylan Lederman, Omar Itani |
| المصدر: | Mathematics, Vol 10, Iss 170, p 170 (2022) Mathematics; Volume 10; Issue 2; Pages: 170 |
| بيانات النشر: | MDPI AG, 2022. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | degeneracy in oscillatory models, Estimation theory, General Mathematics, Degenerate energy levels, MathematicsofComputing_GENERAL, Observable, canonical unidentifiability, Type (model theory), Lambda, extended lambda-omega models, structural identifiability, canonical degeneracy, lambda-omega model, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Computer Science (miscellaneous), QA1-939, Identifiability, Computer Science::Programming Languages, Statistical physics, Inverse function, Degeneracy (mathematics), Engineering (miscellaneous), Mathematics |
| الوصف: | Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (Λ-Ω) models. These are an extension of the classical lambda-omega (λ-ω) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the Λ-Ω models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the Λ-Ω models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of Λ-Ω models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data. |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 2227-7390 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74e54bd39e98c9a46fbcf8c4a4f7b4ad https://www.mdpi.com/2227-7390/10/2/170 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....74e54bd39e98c9a46fbcf8c4a4f7b4ad |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 22277390 |
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