On global identifiability for arbitrary model parametrizations

Set-membership identifiability of nonlinear models and related parameter estimation properties

“…μ-SM-identifiability can be seen as subsuming classical identifiability in the sense that if P * is μ-SM-identifiable, it implies that any p ∈ P * is identifiable in the classical sense (Ljung and Glad, 1994). ε-SM-identifiability is a kind of structural μ-SM-identifiability since subsets of a delimited diameter ε that are SM-identifiable although not μ-SM-identifiable are accepted.…”

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

“…In comparison, there are relatively few techniques available for nonlinear systems (the Taylor series approach [11], similarity transformation based approaches [12,13], and differential algebra techniques) [14,15] and significant computational problems can arise for these, even for relatively simple models [16,17].…”

“…In this paper, four methods are reviewed: a version of the similarity transformation approach for autonomous uncontrolled systems [18], a non-differential input/output observable normal form approach [19], the characteristic set differential algebra approach [14,15], and a recently introduced algebraic input/output relationship approach [19]. Each approach is performed on all of the Pitavastatin pharmacokinetic models developed in order to ascertain whether the unknown system parameters can be identified uniquely or otherwise for the observation available and to compare their performance.…”

“…This approach consists of generating the input/output structure of the given model of the general form (114)-(116) solely in terms of the observation function y and its derivatives using characteristic sets [14,15]. This method requires the model to satisfy the ORC and is implemented using the Rosenfeld-Groebner algorithm in Maple 2010, which calculates a characteristic set for the model with a particular ranking of variables, where one member of the characteristic set gives the input/output map.…”

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

“…A brief overview on techniques for nonlinear identifiability is provided by Boubaker and Fourati [23], but see also the work by Godfrey and Fitch [24] for the use of a Taylor series expansion on examples in pharmacokinetics, publications by Ljung and Glad [25], and Saccomani et al [26] regarding computational approaches using differential algebra, and Evans et al [27] for a method based on the existence of a general nonlinear state transformation.…”