13,065 research outputs found
Observability and Structural Identifiability of Nonlinear Biological Systems
Observability is a modelling property that describes the possibility of
inferring the internal state of a system from observations of its output. A
related property, structural identifiability, refers to the theoretical
possibility of determining the parameter values from the output. In fact,
structural identifiability becomes a particular case of observability if the
parameters are considered as constant state variables. It is possible to
simultaneously analyse the observability and structural identifiability of a
model using the conceptual tools of differential geometry. Many complex
biological processes can be described by systems of nonlinear ordinary
differential equations, and can therefore be analysed with this approach. The
purpose of this review article is threefold: (I) to serve as a tutorial on
observability and structural identifiability of nonlinear systems, using the
differential geometry approach for their analysis; (II) to review recent
advances in the field; and (III) to identify open problems and suggest new
avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods
for Identification and Modelling of Complex Biological Systems" of Complexit
Global Identifiability of Differential Models
Many real-world processes and phenomena are modeled using systems of ordinary
differential equations with parameters. Given such a system, we say that a
parameter is globally identifiable if it can be uniquely recovered from input
and output data. The main contribution of this paper is to provide theory, an
algorithm, and software for deciding global identifiability. First, we
rigorously derive an algebraic criterion for global identifiability (this is an
analytic property), which yields a deterministic algorithm. Second, we improve
the efficiency by randomizing the algorithm while guaranteeing the probability
of correctness. With our new algorithm, we can tackle problems that could not
be tackled before. A software based on the algorithm (called SIAN) is available
at https://github.com/pogudingleb/SIAN
Determining Structurally Identifiable Parameter Combinations Using Subset Profiling
Identifiability is a necessary condition for successful parameter estimation
of dynamic system models. A major component of identifiability analysis is
determining the identifiable parameter combinations, the functional forms for
the dependencies between unidentifiable parameters. Identifiable combinations
can help in model reparameterization and also in determining which parameters
may be experimentally measured to recover model identifiability. Several
numerical approaches to determining identifiability of differential equation
models have been developed, however the question of determining identifiable
combinations remains incompletely addressed. In this paper, we present a new
approach which uses parameter subset selection methods based on the Fisher
Information Matrix, together with the profile likelihood, to effectively
estimate identifiable combinations. We demonstrate this approach on several
example models in pharmacokinetics, cellular biology, and physiology
Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake
In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction–advection–diffusion PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, consideration of spatial analogues of non-spatial models cannot exacerbate structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models
Identification and estimation of continuous time dynamic systems with exogenous variables using panel data
This paper deals with the identification and maximum likelihood estimation of the parameters of a stochastic differential equation from discrete time sampling. Score function and maximum likelihood equations are derived explicitly. The stochastic differential equation system is extended to allow for random effects and the analysis of panel data. In addition, we investigate the identifiability of the continuous time parameters, in particular the impact of the inclusion of exogenous variables
Parameter identifiability and input-output equations
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:
1) identifiability implies input-output identifiability;
2) these notions coincide if the model does not have rational first
integrals;
3) 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.Comment: arXiv admin note: substantial text overlap with arXiv:1910.0396
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