On the Existence of Identifiable Reparametrizations for Linear Compartment Models

Baaijens, Jasmijn A.; Draisma, Jan

doi:10.1137/15m1038013

Cited by 12 publications

(12 citation statements)

References 17 publications

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“…In this paper we focus almost exclusively on "generic" local identifiability and will use the following result to determine generic local identifiability. Recent work from Baaijens [3] shows that the criterion in Proposition 3.3 can be translated to one based on the rank of the bi-adjacency matrix which is order O(|V | 6 ) operations, compared to the method in Proposition 3.3 which is O(|V | 8 ) operations [3].…”

Section: Identifiability Of Input-output Equationsmentioning

confidence: 99%

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Identifiability Results for Several Classes of Linear Compartment Models

2015

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Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.

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Section: Identifiability Of Input-output Equationsmentioning

confidence: 99%

“…Recent work from Baaijens [3] shows that the criterion in Proposition 3.3 can be translated to one based on the rank of the bi-adjacency matrix which is order O(|V | 6 ) operations, compared to the method in Proposition 3.3 which is O(|V | 8 ) operations [3].…”

Section: Identifiability Of Input-output Equationsmentioning

confidence: 99%

Identifiability Results for Several Classes of Linear Compartment Models

2015

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“…Input-output equations have been used to assess structural identifiability for three decades already going back to [21], and several prominent software packages are based on this approach [1,25,17,7,2,3,24,26,16,12,18]. However, it has been known that input-output identifiability is not always the same as identifiability ([10, Example 2.16], [22,Section 5.2]).…”

Section: Introductionmentioning

confidence: 99%

Parameter identifiability and input-output equations

Ovchinnikov¹,

Pogudin²,

Thompson³

2020

Preprint

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Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. One of the standard approaches to assessing this problem is via input-output equations and, in particular, characteristic sets of differential ideals. The precise relation between identifiability and input-output identifiability is subtle. The goal of this note is to clarify this relation. The main results are:• identifiability implies input-output identifiability;• these notions coincide if the model does not have rational first integrals;• the field of input-output identifiable functions is generated by the coefficients of a "minimal" characteristic set of the corresponding differential ideal.We expect that some of these facts may be known to the experts in the area, but we are not aware of any articles in which these facts are stated precisely and rigorously proved.

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“…One of these approaches, which is widely used, is based on input-output equations [3,28,23,13,4,6,27,29,22,24]. Roughly speaking, these are "minimal" equations that depend only on the input and output variables and parameters (for precise definitions via characteristic sets, see Section 4).…”

Section: Introduction 1backgroundmentioning

confidence: 99%

“…Generators of the field of identifiable functions can be further used to reparametrize the model [3,7,21].…”

Section: Introduction 1backgroundmentioning

confidence: 99%

Input-output equations and identifiability of linear ODE models

Ovchinnikov,

Pogudin,

Thompson

2019

Preprint

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Structural identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. The method of input-output equations is one method for verifying structural identifiability. This method stands out in its importance because the additional insights it provides can be used to analyze and improve models. However, its complete theoretical grounds and applicability are still to be established. A subtlety and key for this method to work is knowing if the coefficients of these equations are identifiable.In this paper, to address this, we prove identifiability of the coefficients of input-output equations for types of differential models that often appear in practice, such as linear models with one output and linear compartment models in which, from each compartment, one can reach either a leak or an input. This shows that checking identifiability via input-output equations for these models is legitimate and, as we prove, that the field of identifiable functions is generated by the coefficients of the input-output equations. For a linear compartment model with an input and strongly connected graph, the field of all identifiable functions is generated by the coefficients of the equations obtained from the model just using Cramer's rule, as we show.

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On the Existence of Identifiable Reparametrizations for Linear Compartment Models

Cited by 12 publications

References 17 publications

Identifiability Results for Several Classes of Linear Compartment Models

Identifiability Results for Several Classes of Linear Compartment Models

Parameter identifiability and input-output equations

Input-output equations and identifiability of linear ODE models

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