scholarly journals On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading

2020 ◽  
Author(s):  
Alejandro F. Villaverde ◽  
Gemma Massonis Feixas
Keyword(s):  
Computational Biology ◽  
Dynamic Model ◽  
Symbolic Computation ◽  
Structural Identifiability ◽  
Scaling Method ◽  
Scaling Invariance ◽  
Simple Scaling ◽  
Local Identifiability ◽  
Possible Cause

AbstractA recent paper (Castro M, de Boer RJ, “Testing structural identifiability by a simple scaling method”, PLOS Computational Biology, 2020, 16(11):e1008248) introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may yield a wrong result. Finally, we demonstrate how to analyse structural local identifiability and observability with symbolic computation tools that do not exhibit those issues.

scholarly journals On testing structural identifiability by a simple scaling method: Relying on scaling symmetries can be misleading

2021 ◽  
Vol 17 (10) ◽  
pp. e1009032
Author(s):  
Alejandro F. Villaverde ◽  
Gemma Massonis
Keyword(s):  
Computational Biology ◽  
Dynamic Model ◽  
Structural Identifiability ◽  
Scaling Method ◽  
Scaling Invariance ◽  
Simple Scaling ◽  
Local Identifiability ◽  
Possible Cause

A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not.

scholarly journals The limitations, dangers, and benefits of simple methods for testing identifiability

2021 ◽  
Vol 17 (10) ◽  
pp. e1009425
Author(s):  
Mario Castro ◽  
Rob J. de Boer
Keyword(s):  
Structural Identifiability ◽  
Scaling Method ◽  
Scaling Invariance ◽  
Simple Scaling ◽  
Identifiability Problems

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

scholarly journals Testing structural identifiability by a simple scaling method

2020 ◽  
Vol 16 (11) ◽  
pp. e1008248
Author(s):  
Mario Castro ◽  
Rob J. de Boer
Keyword(s):  
Mathematical Modeling ◽  
General Practitioner ◽  
Empirical Data ◽  
Linear Models ◽  
Biological Processes ◽  
Structural Identifiability ◽  
Scaling Method ◽  
Partially Observed ◽  
Non Linear ◽  
Simple Scaling

Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. A model is said to be structurally unidentifiable, if different quantitative sets of parameters provide the same observable outcome. This is typical (but not exclusive) of partially observed problems in which only a few variables can be experimentally measured. Most of the available methods to test the structural identifiability of a model are either too complex mathematically for the general practitioner to be applied, or require involved calculations or numerical computation for complex non-linear models. In this work, we present a new analytical method to test structural identifiability of models based on ordinary differential equations, based on the invariance of the equations under the scaling transformation of its parameters. The method is based on rigorous mathematical results but it is easy and quick to apply, even to test the identifiability of sophisticated highly non-linear models. We illustrate our method by example and compare its performance with other existing methods in the literature.

Regional estimation of short duration rainfall extremes

1998 ◽  
Vol 37 (11) ◽  
pp. 15-19 ◽  
Author(s):  
V. T. V. Nguyen ◽  
T. D. Nguyen ◽  
H. Wang
Keyword(s):  
Short Duration ◽  
Scale Invariance ◽  
Extreme Rainfall ◽  
Rainfall Data ◽  
Time Interval ◽  
Scaling Method ◽  
Numerical Application ◽  
Rainfall Extremes ◽  
Scale Ratio ◽  
Simple Scaling

The present study proposes a method for estimating the distribution of short-duration (e.g., 1 hour) extreme rainfalls at sites where data for the time interval of interest do not exist, but rainfall data for longer-duration (e.g., 1 day) are available (partially-gaged sites). The proposed method is based on the recently developed “scale-invariance” (or “scaling”) theory. In this study, the scaling concept implies that statistical properties of the extreme rainfall processes for different temporal scales are related to each other by a scale-changing operator involving only the scale ratio. Further, it is assumed that these hydrologic series possess a simple scaling behaviour. The suggested methodology has been applied to extreme rainfall data from a network of 14 recording raingages in Quebec (Canada). The Generalised Extreme Value (GEV) distribution was used to estimate the rainfall quantiles. Results of the numerical application have indicated that for partially-gaged sites the proposed scaling method is able to provide extreme rainfall estimates which are comparable with those based on available at-site rainfall data.

scholarly journals S-synchronization and Excitation Constancy in Structural Identifiability Problem of Nonlinear Systems

2021 ◽  
Vol 248 ◽  
pp. 01004
Author(s):  
Nikolay Karabutov
Keyword(s):  
Nonlinear System ◽  
Nonlinear Dynamical Systems ◽  
Structural Identification ◽  
Structural Identifiability ◽  
Geometric Framework ◽  
Nonlinear Dynamical ◽  
Nonlinear Part ◽  
System A ◽  
Local Identifiability ◽  
Identifiability Problem

An approach to analysis the structural identifiability (SI) of nonlinear dynamical systems under uncertainty was proposed. S-synchronizability condition of an input is the basis for the structural identifiability estimation of the nonlinear system. A method for obtaining a set containing information about the nonlinear part of the system wasproposed. The decision on SI of the system was based on the analysis of geometric frameworks reflected the state of the system nonlinear part. Geometric frameworks were defined on the specified set. Conditions for structural indistinguishability of geometric frameworks and local identifiability of the nonlinear part were obtained. It shown that a non-S-synchronizing input gives an insignificant geometric framework. This input is a sign of structural non-identifiability of the nonlinear system. The method for estimating the structural identifiability of the nonlinear system was proposed. We show that the structural identifiability is the basis for structural identification of the system. The structural identifiability degree was introduced, and the method of its estimation was proposed.

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