The DOI matches its Crossref record; 28 of the 29 references it cites were found in a registry or an index; 1 of the 12 sources its claims cite were checked for support.
Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood
Open accessAbstract
MOTIVATION: Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis. RESULTS: We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used for experimental planning and for model reduction. AVAILABILITY: An implementation is freely available for MATLAB and the PottersWheel modeling toolbox at http://web.me.com/andreas.raue/profile/software.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper presents a profile-likelihood method for assessing structural and practical identifiability in partially observed dynamical models and for deriving likelihood-based confidence intervals. Applied to a JAK-STAT signaling model, it identifies four structurally non-identifiable parameters and one practically non-identifiable parameter, and shows how additional measurements can resolve these ambiguities.
Key findings
- Profile likelihood distinguishes structural non-identifiability, seen as a flat profile, from practical non-identifiability, seen as a profile with a minimum that fails to cross the confidence threshold in one or both directions; identifiable parameters cross the threshold on both sides.
- In the JAK-STAT application, parameters p2, x1(0), s1, and s2 were structurally non-identifiable, with functional relations p2·x1(0)=const, s1·x1(0)=const, and s2·x1(0)=const; p3 was practically non-identifiable for increasing values.
- Table 1 reports infinite likelihood-based intervals for the structurally non-identifiable parameters, whereas Hessian-based asymptotic intervals were finite but misleadingly narrow, e.g. p2: −33 to +31, x1(0): −31 to +32, s1: −32 to +31, s2: −32 to +31; for p3, the profile-likelihood interval was −1.14 to +∞ versus −1.14 to +0.15 from the Hessian.
- Adding hypothetical measurements of x1(0)=200±20 nM and x3/(x2+x3)=0.90±0.05 at t=20 min made p2, x1(0), s1, and s2 structurally identifiable and p3 practically identifiable, while p2 remained practically non-identifiable. Profile-likelihood computation took 54±18 s per parameter on a 1 GHz CPU with 2 GB RAM.
Methods
- The approach uses an ODE model with weighted least-squares objective χ², computes the profile likelihood for each parameter by re-optimizing all other parameters at fixed values of the target parameter, and derives likelihood-based confidence intervals from χ² thresholds.
- The application is a JAK-STAT signaling model inspired by Swameye et al., calibrated to experimental data; observables are phosphorylated STAT in cytoplasm (y1) and total STAT in cytoplasm (y2) measured by quantitative western blotting, with cytoplasm and nucleus volumes of 1400 µm³ and 450 µm³.
- Parameters calibrated include p1–p4, s1, s2, and x1(0), with x2(0)–x4(0) set to zero; the model was implemented and fitted with PottersWheel, and experimental planning and model reduction were explored via profile-likelihood trajectories, Monte Carlo simulations, and likelihood-ratio thresholds.
Limitations
- The authors state that structural non-identifiability cannot be resolved by refining existing measurements or reducing noise; it requires a qualitatively new measurement that changes the observation mapping, such as observing additional species. Practical non-identifiability can be resolved by increasing the amount or quality of data and/or selecting better measurement time points.
- The authors note that recovering functional relations unambiguously from parameter changes along the profile likelihood is only possible when the corresponding manifold is one-dimensional; higher-dimensional manifolds require further analysis, such as the approach of Hengl et al.
- Evident from the text: the method is demonstrated on a single JAK-STAT model and dataset, with no broad empirical comparison across many model classes; the approach also assumes a sufficiently adequate model and normally distributed measurement noise.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
1 of 12 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The largest discrepancy occurs for practically non-identifiable parameters, where asymptotic confidence intervals are significantly smaller than likelihood-based confidence intervals.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The variability of the predicted model observables y along the profile likelihood of p 3 remains consistent with the measurement errors, as shown in Figure 6.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The resulting plots of profile likelihood versus parameter reveal four structurally non-identifiable parameters p 2 , x 1 (0), s 1 , s 2 by their flat profile likelihood, see Figure 3, upper panel.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: An appropriate model M that sufficiently describes the available experimental data is assumed.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For identifiable parameters the discrepancies are small.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The functional relations h connecting these structurally non-identifiable parameters can be recovered from the changes of the remaining parameters, while calculating the profile likelihood of the structurally non-identifiable parameters, as shown in Figure 4.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The recalculated profile likelihood reveals, that parameters p 2 , x 1 (0), s 1 , s 2 become structurally identifiable (Fig. 3, lower panel), by measuring only one of them.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The profile likelihood reveals that parameter p 3 is practically non-identifiable for increasing parameter values.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: An appropriate model M that sufficiently describes the available experimental data is assumed.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Nevertheless, a lower confidence bound can be derived.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In this case, asymptotic approximation leads to large but nevertheless finite confidence intervals for the structurally non-identifiable parameters.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“All internal model states can only be identified up to a common factor.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- It may state two separate claims as one. 14
- Probably not a substantial claim. 13
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“An approach to detect structural non-identifiability by the corresponding functional relations was introduced by Hengl et al. (2007).It is able to detect flatness of likelihood for arbitrary models, but it is not intended to detect practical non-identifiability.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
- Partly supportedcites Hengl et al., 2007 sourceExperimental — accuracy not yet measured
The Approach and Conclusion describe detecting structural non-identifiability through functionally related parameters in nonlinear models. But the Introduction explicitly lists practical identifiability analysis, accounting for data quality, as an aim of the method, contrary to the claim that it is not intended for that purpose. The passages do not specifically describe the method as detecting likelihood flatness. (LLM, conf=0.90)
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Partly supported
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Spots of largest variability suggest where and when a measurement of a species most efficiently determines theses parameters: x 1 at times t = 0 or t > 50; x 2 to x 4 at times 5 < t < 30.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Calculating the profile likelihood takes 54 ± 18 s per parameter, using an implementation of the approach embedded in the Potters-Wheel fitting toolbox (1 GHz CPU, 2 GB RAM), which is described in the Supplementary Material.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Parameter p 3 becomes practically identifiable, only previously structurally non-identifiable parameter p 2 remains practically non-identifiable.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The trajectories of the internal model states x along the profile likelihood of the practically non-identifiable parameter p 3 shown in Figure 6 comprises large antipodal variability of species x 2 and x 3 , revealing that the experimental setup is inappropriate to estimate this parameter with confidence.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“h 1 (θ sub ) = p 2 •x 1 (0)-const = 0 h 2 (θ sub ) = s 1 •x 1 (0)-const = 0 ( 1 1 ) h 3 (θ sub ) = s 2 •x 1 (0)-const = 0”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The approach was applied to a model of the JAK-STAT signaling pathway.Non-identifiable parameters were detected, revealing limitations in the experimental setup.Additional measurements that efficiently improve parameter identification were suggested and validated.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“They are exact if the observables y depend linearly on θ.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.1 Asymptotic confidence intervals
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“Unfortunately, these methods become rapidly infeasible with increasing model size (Margaria et al., 2001;White et al., 2001).Practical non-identifiability cannot be detected, since experimental data are disregarded.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Even identifiable parameters can only be determined within confidence intervals, which contain the true value of the parameter with a desired probability (Lehmann and Leo, 1983).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 1 INTRODUCTION
What the sources say
- Not matchedcites Lehmann and Leo, 1983
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- Not matched
None of the sources cited for this claim have been checked yet.
In the paper
“These methods are appropriate if functional relations h between the parameters emerging from structural non-identifiability are linear.This is often not the case for reaction networks modeled by ODE, because observables depend non-linearly on the parameters.Practical non-identifiability cannot be detected, because a quadratic approximation is not able to explain increasing but limited behavior of”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“However, even for the simplest reaction network the observables y depend nonlinearly on θ and the amount and quality of experimental data is often insufficient.Therefore, asymptotic confidence intervals might not be appropriate (Joshi et al., 2006).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.1 Asymptotic confidence intervals
What the sources say
- Not checked — no full text of the sourcecites Joshi et al., 2006 source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Likelihood-based confidence intervals are considered superior to asymptotic confidence intervals for finite samples (Neale and Miller, 1997).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.2 Finite sample confidence intervals
What the sources say
- Not checked — no full text of the sourcecites Neale and Miller, 1997 source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Along a practical non-identifiability, the observable y change only negligibly remaining compliant with the given measurement accuracy.Nevertheless, model behavior in terms of internal states x might vary strongly.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > )]:
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This arises frequently if amount and quality of experimental data is insufficient and manifests in a confidence interval that is infinite.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.3.2 Practical non-identifiability
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“The points of passover represent likelihoodbased confidence intervals as defined in Equation ( 8) (Royston, 2007).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 4 APPROACH
What the sources say
- Not checked — no full text of the sourcecites Royston, 2007 source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The results are easy to interpret”
- Also stated in: § 6 DISCUSSION · plain
“The approach results in easily interpretable plots of profile likelihood versus parameter.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Abstract
Strength:plain· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
- Also stated in: § 6 DISCUSSION · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The profile likelihood of a practically non-identifiable parameter has a minimum, but is not excessing a threshold α for increasing and/or decreasing values of θ i (see Definition 1).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 4 APPROACH
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This gives insight into a complex and high-dimensional parameter space.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It can be automated, but an explicit advantage is that the output might be evaluated visually.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
Strength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The approach can be applied to any parameter estimation problem, where a likelihood or a similar objective criterion is available, e.g.partial differential equations (PDE) or stochastic differential equations (SDE).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The profile likelihood can be calculated for each parameter separately.Thereby it is possible to restrict the analysis to the parameters relevant for the biological question.Moreover, this allows to perfectly parallelize the approach, which is a major benefit for its scalability.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Working in logarithmic parameter space linearizes the functional relations given in Equation (11).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The impact of new measurements can be evaluated by Monte Carlo simulations.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, identifiability analysis ensures that the model complexity is tailored to the information content given by the experimental data.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
The authors state this as an assumption.
The measurement noise is normally distributed.
“The measurement noise (t) is assumed to be normally distributed.”
The authors state this as an assumption.
An appropriate model M that sufficiently describes the available experimental data is assumed.
“Furthermore, an appropriate model M that sufficiently describes the available experimental data is assumed.”
The paper relies on this without support.
No approach for explicit testing of practical non-identifiability is available.
“Similar to a clear formal definition, an approach for explicit testing of practical non-identifiability is not available to our knowledge.”
The authors state this as an assumption.
The initial values of species x2 to x4 are equal to zero.
“The initial values of species x 2 to x 4 are assumed to be equal to zero.”
The authors state this as an assumption.
For the model-reduction argument, a parameter θi is practically non-identifiable for decreasing parameter value.
“Assume that a parameter θ i is practically non-indentifiable for decreasing parameter value.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Such parameter estimations usually yield statistical information related to parameter precision (importantly, not accuracy) such as standard errors or correlation matrices, and sometimes information derived from more sophisticated approaches such as profile likelihood.39”
From Best Practices to Maximize the Use and Reuse of Quantitative and Systems Pharmacology Models: Recommendations From the United Kingdom Quantitative and Systems Pharmacology Network (2019) · cites this paper as [39]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Raue et al. (2009) referred to likelihood ratio C.I.s as finite sample C.I.s, to underscore the superiority of likelihood ratio C.I.s over Wald-type C.I.s.”
From rSalvador: An R Package for the Fluctuation Experiment (2017) · cites this paper as Raue et al. 2009
In the citing paper
“When two models are nested (Mð hPL Þ and Mð hopt Þ) their likelihood ratio is approximately distributed according to a v 2 p distribution.Here p refers to the number of degrees of freedom which is defined as the difference in the number of parameters (which in this case is 1).”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“In such cases, more reliable confidence intervals can be obtained using the Profile Likelihood method [36].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“Techniques for this exist in both a frequentist [13,36,91] as well as a Bayesian setting [87,90].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“Fortunately, recent literature is correcting this (e.g. [129–140]).”
From Reverse engineering and identification in systems biology: strategies, perspectives and challenges (2014) · cites this paper as [133]
In the citing paper
“Given the data, not all parameters are identifiable (Raue et al., 2009).”
From A bayesian approach to targeted experiment design (2012) · cites this paper as Raue et al., 2009
In the citing paper
“Methods for an approximate sampling of the parameter space, e.g. the Markov Chain Monte Carlo (MCMC) methods [11,12], and bootstrap based approaches [4,13] are numerically demanding and provide only rough approximations for ODE models. Therefore, it is difficult to control the coverage of the prediction confidence intervals for such approaches.”
From Likelihood based observability analysis and confidence intervals for predictions of dynamic models (2012) · cites this paper as [4]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Concentration unit conflicts with figure labels
MinorThe text says concentrations are modeled in nanometers, a unit of length, while the figure labels use nM, a unit of concentration.
“Species concentrations are modeled in nanometer.”
“time / min x 1 / nM”
Citations
Cites
Press, W. H., Teukolsky, S. L. A., Flannery, B. P., & Vetterling, W. T. (1990) · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · Cited by 6,980
Ziegel, E. R., Lehmann, E. L., & Casella, G. (1999) · Technometrics · doi:10.2307/1270597 · Cited by 4,203
Lehmann, E. L. (1983) · Springer eBooks · doi:10.1007/978-1-4757-2769-2 · Cited by 1,357
Murphy, S. A., & Van Der Vaart, A. W. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10474219 · Cited by 712
On global identifiability for arbitrary model parametrizations
Lennart Ljung, A., & Glad, T. (1994) · Automatica · doi:10.1016/0005-1098(94)90029-9 · Cited by 644
A method for computing profile-likelihood-based confidence intervals
Venzon, D. J., & Moolgavkar, S. H. (1988) · Applied Statistics · doi:10.2307/2347496 · Cited by 565
Systems biology toolbox for matlab: a computational platform for research in systems biology
Schmidt, H., & Jirstrand, M. (2006) · Bioinformatics · doi:10.1093/bioinformatics/bti799 · Cited by 473
System identifiability based on the power series expansion of the solution
Pohjanpalo, H. (1978) · Mathematical Biosciences · doi:10.1016/0025-5564(78)90063-9 · Cited by 440
Parameter and structural identifiability concepts and ambiguities: a critical review and analysis
Cobelli, C., & DiStefano, J. J. (1980) · American Journal of Physiology-Regulatory, Integrative and Comparative Physiology · doi:10.1152/ajpregu.1980.239.1.r7 · Cited by 402
Swameye, I., Müller, T. G., Timmer, J., Sandra, O., & Klingmüller, U. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0237333100 · Cited by 316
Self-citation
Flagged first, then by citations
1 of the 29 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Items 801–900 of 1,414
Lele, S. R., Glen, C. G., & Ponciano, J. M. (2025) · Entropy · doi:10.3390/e27030289 · Cited by 5
“However, it would be a major advantage if a method provided diagnostics for potential non-identifiability (e.g., [40]).”
A multi-inverse approach for a holistic understanding of applied animal science systems
Vargas-Villamil, L. M., Tedeschi, L. O., Medina-Peralta, S., Izquierdo-Reyes, F., Alberto, J. A. N., & González-Gardúño, R. (2020) · animal · doi:10.1017/s1751731120000877 · Cited by 5
Tumorigenesis and axons regulation for the pancreatic cancer: A mathematical approach
Chauvet, S., Hubert, F., Mann, F., & Mezache, M. (2022) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2022.111301 · Cited by 6
Stoudt, S., de Valpine, P., & Fithian, W. (2023) · Journal of Statistical Theory and Practice · doi:10.1007/s42519-023-00336-5 · Cited by 5
Murphy, R. J., Gunasingh, G. P., Haass, N. K., & Simpson, M. J. (2023) · Bulletin of Mathematical Biology · doi:10.1007/s11538-023-01229-1 · Cited by 6
“To specify initial conditions we introduce V m ( T ) = V 1 ( T ) as the volume of melanoma cells at spheroid formation, t = T , and treat this as a parameter.”
Lang, P. F., Penas, D. R., Banga, J. R., Weindl, D., & Novák, B. (2024) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011151 · Cited by 5
Liu, Y., Warne, D. J., & Simpson, M. J. (2024) · Physical review. E · doi:10.1103/physreve.110.044405 · Cited by 5
“Using maximum likelihood estimation and the profile likelihood [24, 25, 26, 27, 28], we obtain best-fit parameter estimates and likelihood-based confidence intervals that allow us to examine the practical identifiability of parameter estimates derived from noisy count data.”
MethodMirzaei, N. M., Kevrekidis, P. G., & Shahriyari, L. (2024) · Royal Society Open Science · doi:10.1098/rsos.240718 · Cited by 5
“Then we calculate the profile likelihood (see [102]) of each parameter, i.e., PL ( θ i ) .”
Klett, H., Rodriguez-Fernández, M., Dineen, S. M., Leon, L. R., Timmer, J., & Doyle, F. J. (2014) · Mathematical Biosciences · doi:10.1016/j.mbs.2014.07.011 · Cited by 5
Self-citationCarta, A., Madalena Chaves, A., & Gouzé, J. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-33636-2_8 · Cited by 5
“Whether or not parameters can be estimated uniquely depends on the model structure, the parameterization of the model and the experiment used to get the data [26].”
BackgroundA comparison of methods for extracting influenza viral titer characteristics
González‐Parra, G., Rodriguez, T., & Dobrovolny, H. M. (2016) · Journal of Virological Methods · doi:10.1016/j.jviromet.2016.02.005 · Cited by 5
Kamoi, S., Squire, D. T., Revie, J. A., et al. (2014) · IFAC Proceedings Volumes · doi:10.3182/20140824-6-za-1003.01104 · Cited by 5
“However, identification of the model parameters becomes much more difficult if not impossible, eliminating their use in practical application based patient-specific context, while increasing their use as models for understanding (Docherty et al., 2011, Raue et al., 2009).”
MethodHigh-Throughput Data Pipelines for Metabolic Flux Analysis in Plants
Poskar, C. H., Huege, J., Krach, C., et al. (2013) · Methods in molecular biology · doi:10.1007/978-1-62703-688-7_14 · Cited by 5
Fachet, M., Flassig, R., Rihko‐Struckmann, L., & Sundmacher, K. (2017) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.7b01423 · Cited by 5
Mathematical modeling and quantitative analysis of HIV-1 Gag trafficking and polymerization
Liu, Y., & Zou, X. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005733 · Cited by 5
Saucedo, O., Martcheva, M., & Annor, A. (2019) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2019174 · Cited by 5
“If the graph of the profile likelihood is constant on a certain interval or stays below a fixed threshold, we classify that parameter to be practically unidentifiable [44].”
BackgroundTönsing, C., Timmer, J., & Kreutz, C. (2019) · Frontiers in Physics · doi:10.3389/fphy.2019.00149 · Cited by 5
“Both structures are typical cases of either structural or practical nonidentifiabilities in the likelihood [8, 11], which are a consequence of over-parameterization of the model or appear when the information provided by the available data is not sufficient to restrict parameters to finite confidence intervals, respec…”
BackgroundSelf-citationvan Stee, M. F., Krishnan, S., Groen, A. K., & de Graaf, A. A. (2019) · BMC Biomedical Engineering · doi:10.1186/s42490-019-0030-z · Cited by 5
“Parameter identifiability analysis To investigate the reliability of the obtained parameter estimates (kp2, kp3, kp4 and A), parameter identifiability analysis using PL [31] was performed.”
BackgroundMethodInfluentialTantau, M., Popp, E., Perner, L., Wielitzka, M., & Ortmaier, T. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2020.12.1400 · Cited by 5
“Physically motivated models, mostly called bright greybox models of electric drive trains with coupled mechanics are commonly used in industry for control design (Schütte (2003)), simulation, feed-forward, model-based fault diagnosis (Witczak et al. (2002)) etc.”
MethodInfluentialStructural identifiability of linear Port Hamiltonian systems
Medianu, S., & Lefèvre, L. (2021) · Systems & Control Letters · doi:10.1016/j.sysconle.2021.104915 · Cited by 5
Modelling and Control of Epidemics Across Scales
Hernandez-Vargas, E. A., González, A. H., Beck, C. L., Bi, X., Campana, F. C., & Giordano, G. (2022) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc51059.2022.9992380 · Cited by 6
“different parameter analysis such as computation of likelihood profiles [104], parametric bootstrapping and confidence intervals [105], along with direct visualization of the results.”
MethodLikelihood-based estimation and prediction for a measles outbreak in Samoa
Wu, D. H., Petousis‐Harris, H., Paynter, J., Suresh, V., & Maclaren, O. J. (2023) · Infectious Disease Modelling · doi:10.1016/j.idm.2023.01.007 · Cited by 4
“Additionally, limitations in data collection, combined with complex model structures, may mean parameter estimates are not uniquely determinable, or nonidentifiable (Raue et al., 2009; Fr€ohlich et al., 2014).”
BackgroundStudy design and parameter estimability for spatial and temporal ecological models
Peacock, S. J., Krkošek, M., Lewis, M. A., & Lele, S. R. (2016) · Ecology and Evolution · doi:10.1002/ece3.2618 · Cited by 4
“…two sources: a) structural nonidentifiability, a problem, that is, associated with the structure of the model that is being fitted, and b) practical nonidentifiability, also called nonestimability arising from the inadequacy of the particular data at hand (Campbell & Lele, 2014; Raue et al., 2009).”
Estimating uncertainty of model parameters obtained using numerical optimisation
Brastein, O. M., Lie, B., Pfeiffer, C., & Skeie, N.-O. (2019) · Modeling, Identification and Control · doi:10.4173/mic.2019.4.3 · Cited by 4
Delannée, V., Langouët, S., Théret, N., & Siegel, A. (2017) · PeerJ · doi:10.7717/peerj.3703 · Cited by 5
“From this set of parameters, a trust-region algorithm is applied iteratively to decrease the following mean-square distance (Raue et al., 2009), where σk,l,i’s depict an internal error linked to the parameter estimation process. χ2(θ)= 8∑ k=1 2∑ l=1 3∑ i=1 ( yobsk,l,i−yk(θ,tl,di) σk,l,i )2 .”
MethodFast Inference for Network Models of Infectious Disease Spread
Romanescu, R. G., & Deardon, R. (2017) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12270 · Cited by 5
“…method works by inverting a likelihood ratio test for each parameter to find a range, about the MLE, where the log likelihood does not drop more than a certain amount (see, e.g. Raue et al. , 2009); a drop of 1.92 corresponds to a 95% CI for the parameter being profiled (Stryhn & Christensen, 2003).”
MethodInfluentialModeling Formalisms in Systems Biology of Apoptosis
Kallenberger, S. M., & Legewie, S. (2012) · Springer eBooks · doi:10.1007/978-1-4614-4009-3_1 · Cited by 6
Two parallel pathways implement robust propionate catabolism and detoxification in mycobacteriaPreprint
Tummler, K., Zimmermann, M., Schubert, O. T., Aebersold, R. H., Kühn, C., Sauer, U., & Klipp, E. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/258947 · Cited by 5
Tumor cell total mRNA expression shapes the molecular and clinical phenotype of cancerPreprint
Cao, S., Wang, J. R., Ji, S., Peng, Y., Montierth, M. D., Guo, S., Shen, J. P., Zhao, X. L., Chen, J., Lee, J. J., et al. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.09.30.306795 · Cited by 5
de Rooij, M., van Riel, N. A. W., & O’Donovan, S. D. (2025) · npj Systems Biology and Applications · doi:10.1038/s41540-025-00570-6 · Cited by 5
An SIR‐based Bayesian framework for COVID‐19 infection estimation
Wu, H., Stephens, D. A., & Moodie, E. E. M. (2024) · Canadian Journal of Statistics · doi:10.1002/cjs.11817 · Cited by 4
“In this case, the likelihood reduces to: The profile likelihood method (Murphy and van der Vaart, 2000; Raue et al., 2009) is used to assess the parameter identifiability when only seroprevalence survey data are available.”
Coral bleaching dynamics on the Great Barrier Reef: New insights from a mathematical model
Brown, K. M., Araujo, R. P., Corry, P., et al. (2025) · Ecological Modelling · doi:10.1016/j.ecolmodel.2025.111110 · Cited by 4
Unidentified and Confounded? Understanding Two-Tower Models for Unbiased Learning to Rank
Hager, P., Zoeter, O. R., & de Rijke, M. (2025) · ACM SIGIR International Conference on Theory of Information Retrieval (ICTIR) · doi:10.1145/3731120.3744604 · Cited by 4
On the different flavours of practical identifiability
Heinrich, M., Arutjunjan, R., & Timmer, J. (2025) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2025.100556 · Cited by 4
Self-citationA calibration framework to improve mechanistic forecasts with hybrid dynamic models
Boussange, V., Aceituno, P. V., Schäfer, F., et al. (2025) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.70190 · Cited by 4
Frank, R., Gabel, M., Heiss, K., Mueller, A., & Graw, F. (2018) · Frontiers in Immunology · doi:10.3389/fimmu.2018.01137 · Cited by 5
“Identifiability of parameter estimates was assessed using profile likelihood analysis (28) with estimates shown in Figure A2.”
MethodAbout Model Validation in Bioprocessing
Rajamanickam, V., Babel, H., Herrera, L. M., Ehsani, A., Stiefel, F., Haider, S., Presser, B., & Knapp, B. L. (2021) · Processes · doi:10.3390/pr9060961 · Cited by 7
“Under the assumption of independent and normal distributed error terms this directly leads to the residual sum of squares (RSS), weighted by the variance of the error term [53].”
MethodDetermining Losses in Jet Injection Subcutaneous Insulin Delivery: A Model-Based Approach
McHugh, A. D., Chase, J. G., Knopp, J. L., Zhou, T., & Holder-Pearson, L. R. (2022) · Journal of Diabetes Science and Technology · doi:10.1177/19322968221085032 · Cited by 4
Modeling unveils sex differences of signaling networks in mouse embryonic stem cells
Sultana, Z., Dorel, M., Klinger, B., Sieber, A., Dunkel, I., Blüthgen, N., & Schulz, E. G. (2023) · Molecular Systems Biology · doi:10.15252/msb.202211510 · Cited by 3
“To this end, we performed profile likelihood calculation for the parameters of both cell line models (Raue et al , 2009).”
MethodVelluet, J., Noce, A. D., & Letort, V. (2023) · Plant Phenomics · doi:10.34133/plantphenomics.0133 · Cited by 4
“…are a local, and partial, quantification of practical identifiability analysis since all measurements are considered as perfect (no noise), (b) profile likelihood-based confidence interval [29] that we propose to turn into a quantitative risk index instead of a binary indicator, and (c) ARE [18].”
BackgroundMethodInfluentialMirzaei, N. M., & Shahriyari, L. (2024) · Physical Biology · doi:10.1088/1478-3975/ad2777 · Cited by 4
“Raue et al define a non-identifiable parameter as a parameter that is a unique minimum of the likelihood function, but its confidence interval/region is infinite [44].”
Alyami, L., Das, S., & Townley, S. (2024) · PLOS Global Public Health · doi:10.1371/journal.pgph.0003467 · Cited by 4
Salmaniw, Y., & Browning, A. P. (2025) · Journal of Mathematical Biology · doi:10.1007/s00285-025-02225-w · Cited by 4
“Tools for the assessment of structural identifiability are now well established for ordinary differential equation (ODE) models (Bellu et al. 2007; Raue et al. 2009; Chis et al. 2011; Barreiro and Villaverde 2023), and are, perhaps, most pertinent in scenarios where only partial observations of the…”
Data-informed model reduction for inference and prediction from non-identifiable models
Simpson, M. J. (2025) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2025.112155 · Cited by 4
Identifiability of phenotypic adaptation from low-cell-count experiments and a stochastic model
Browning, A. P., Crossley, R. M., Villa, C., Maini, P. K., Jenner, A. L., Cassidy, T., & Hamis, S. (2025) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1013202 · Cited by 5
Karami, H., Bleichrodt, A., Luo, R., et al. (2025) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-025-03208-z · Cited by 4
Robust global identifiability theory using potentials—Application to compartmental models
Wongvanich, N., Hann, C. E., & Sirisena, H. (2015) · Mathematical Biosciences · doi:10.1016/j.mbs.2015.01.013 · Cited by 4
Basis Function Modelling of Respiratory Patients with High or Low Auto-PEEP
Langdon, R., Docherty, P. D., & Chase, J. G. (2017) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2017.08.2246 · Cited by 4
Contribution of external resistance to mass transfer during pasta drying
Mercier, S. (2018) · Drying Technology · doi:10.1080/07373937.2018.1437546 · Cited by 4
“The confidence interval of the least square estimate was quantified for each model and sample of pasta using the profile likelihood method.([26]) Previous works have shown that this nonlinear uncertainty approach can accurately quantify the simultaneous confidence intervals of the transport coefficients from measureme…”
MethodStochastic nonlinear model for somatic cell population dynamics during ovarian follicle activation
Clément, F., Robin, F., & Yvinec, R. (2021) · Journal of Mathematical Biology · doi:10.1007/s00285-021-01561-x · Cited by 4
More Identifiable yet Equally Performant Transformers for Text Classification
Bhardwaj, R., Majumder, N., Poria, S., & Hovy, E. H. (2021) · doi:10.18653/v1/2021.acl-long.94 · Cited by 7
Wiesner, M., Schäfer, K., Bergmann, W., Berger, A., Shulpyakov, P., Dittert, C., & Büskens, C. (2021) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2021.10.320 · Cited by 4
Large-deposit non-linear chemical reactive flows in porous media: Identifiability and observability
Yang, S., Russell, T., JUNIOR, A. S. L. V., & Bedrikovetsky, P. (2022) · Journal of Natural Gas Science and Engineering · doi:10.1016/j.jngse.2022.104611 · Cited by 4
Schmeckenbecher, J., Rattner, K., Cramer, R. J., Plener, P. L., Baran, A., & Kapusta, N. D. (2022) · BJPsych Open · doi:10.1192/bjo.2022.526 · Cited by 5
DISCREPANCY MODELING FOR MODEL CALIBRATION WITH MULTIVARIATE OUTPUT
White, A., & Mahadevan, S. (2023) · International Journal for Uncertainty Quantification · doi:10.1615/int.j.uncertaintyquantification.2023044543 · Cited by 4
Chen, J. H., Fukasawa, M., Sakane, N., Suganuma, A., Kuzuya, H., Pandey, S., D’Alessandro, P., Venkatapurapu, S. P., & Dwivedi, G. (2023) · PLoS ONE · doi:10.1371/journal.pone.0287069 · Cited by 4
González‐Parra, G., Villanueva-Oller, J., Navarro-González, F. J., Ceberio, J., & Luebben, G. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114695 · Cited by 5
Babaev, D. S., Kutumova, E. O., & Kolpakov, F. (2025) · Frontiers in Systems Biology · doi:10.3389/fsysb.2025.1504077 · Cited by 5
Necessary and Sufficient Conditions for State-Space Network Realization
Paré, & Philip, E. (2014) · ScholarsArchive (Brigham Young University) · Cited by 4
Parameter estimation in tree graph metabolic networks
Astola, L., Stigter, J. D., Roldán, M. V. G., van Eeuwijk, F. A., Hall, R. D., Groenenboom, M. A. C., & Molenaar, J. J. (2016) · PeerJ · doi:10.7717/peerj.2417 · Cited by 4
“Structural identifiability does not imply practical identifiability and therefore we have studied the practical identifiability of the parameters in our system by means of profile likelihood (Raue et al., 2009).”
MethodThe quadratic dimensional reduction method for parameter identification
Poole, M., Murray, R., Davidson, S. M., et al. (2019) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2019.03.001 · Cited by 4
Verification and Validation Principles from a Systems Perspective
Murray-Smith, D. J. (2019) · Simulation foundations, methods and applications · doi:10.1007/978-3-319-70766-2_4 · Cited by 4
Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour
Brastein, O. M., Sharma, R., & Skeie, N. (2019) · Linköping electronic conference proceedings · doi:10.3384/ecp2017051 · Cited by 4
“…`PL (θi) is defined as the minimum log likelihood for θi when the remaining parameters are freely optimised (Raue et al., 2009; Venzon and Moolgavkar, 1988): `PL (θi) = min θ j 6=i g ( θ j 6=i;M ,K ,θi ) (4) Values of θi must be chosen prior to optimising the remaining θ j 6=i (Raue et al., 2009).”
BackgroundMethodInfluentialA neural network assisted Metropolis adjusted Langevin algorithm
Müller, C. A., Diedam, H., Mrziglod, T., et al. (2020) · Monte Carlo Methods and Applications · doi:10.1515/mcma-2020-2060 · Cited by 4
State Estimation Model Reduction Through the Manifold Boundary Approximation Method
Švenda, V. G., Transtrum, M. K., Francis, B. L., et al. (2021) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2021.3091547 · Cited by 4
Parvinian, B., Bighamian, R., Scully, C. G., Hahn, J., & Pathmanathan, P. (2021) · Frontiers in Physiology · doi:10.3389/fphys.2021.705222 · Cited by 4
“The test for structural soundness is known as structural or theoretical identifiability (Pronzalo and Walter, 1997; Raue et al., 2009).”
BackgroundInfluentialEnhanced profile likelihood method for the nonstationary hydrological frequency analysis
Vidrio‐Sahagún, C. T., & He, J. (2022) · Advances in Water Resources · doi:10.1016/j.advwatres.2022.104151 · Cited by 4
THE BETA-WEIBULL DISTRIBUTION ON THE LATTICE OF INTEGERS
Nekoukhou, V., Bidram, H., & Roozegar, R. (2016) · Ciência e Natura · doi:10.5902/2179460x21864 · Cited by 4
“In view of the fact that the above confidence intervals are finite, we can conclude that the parameters of the distribution in question are identifiable; see Raue et al. (2009).”
BackgroundIdentifiability of Patient Effort Respiratory Mechanics Model
Chee, J. Z., Chiew, Y. S., Tan, C. P., & Arunachalam, G. (2018) · IEEE-EMBS Conference on Biomedical Engineering and Sciences · doi:10.1109/iecbes.2018.8626625 · Cited by 4
“This paper presents the investigation of the polynomial model stability and identifiability [8, 9].”
BackgroundMethodInfluentialApplying a Statistical Model to the Observed Texture Evolution of Fatigued Metal Films
Pedretscher, B., Nelhiebel, M., & Kaltenbacher, B. (2020) · IEEE Transactions on Device and Materials Reliability · doi:10.1109/tdmr.2020.3004044 · Cited by 4
“In literature, local approximations based on the Hessian of the likelihood, sampling based approaches as MCMC simulations, and profile likelihoods [13]–[16] can be used to compute the CIs of the parameters.”
MethodStructural identifiability of battery equivalent circuit models.Preprint
Alavi, S. M. M., Mahdi, A., Payne, S. J., et al. (2015) · arXiv (Cornell University) · Cited by 4
Stein, A. M. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/123240 · Cited by 4
“Thus we recommend that pharmacometricians regularly use bootstrapping or likelihood profiling [5] as an additional check.”
BackgroundMethodInfluentialMaximum Entropy Framework For Inference Of Cell Population Heterogeneity In Signaling NetworksPreprint
Dixit, P. D., Lyashenko, E., Niepel, M., & Vitkup, D. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/137513 · Cited by 4
Observability and Structural Identifiability of Nonlinear Biological SystemsPreprint
Villaverde, A. F. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1812.04525 · Cited by 4
“These properties may also be analysed with other symbolic approaches, such as power series [11, 48, 76], differential algebra [4, 16, 26, 38, 43], or others [15, 66, 78], to name just a few, as well as with semi-numerical [33, 56] or numerical approaches [53, 60].”
BackgroundJohn, W., Stewart, W. C., Jayaprakash, C., & Das, J. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.03.17.484491 · Cited by 4
“The task of estimating parameters is challenging due to a variety of reasons (Stewart (2018); Ashyraliyev et al. (2009); Raue et al. (2009)), one of which is that the number of model parameters is largerthanthatoftheavailabledata.”
BackgroundReaction-diffusion patterning of DNA-based artificial cellsPreprint
Leathers, A., Walczak, M., Brady, R. A., et al. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.03.24.485404 · Cited by 4
Optimal Experiment Design, Fisher Information
Kreutz, C., & Timmer, J. (2013) · Springer eBooks · doi:10.1007/978-1-4419-9863-7_1222 · Cited by 4
Self-citationActivator-blocker model of transcriptional regulation by pioneer-like factorsPreprint
Riesle, A. J., Gao, M., Rosenblatt, M., et al. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.01.11.523615 · Cited by 4
Self-citationQuantifying single-cell diacylglycerol signaling kinetics after uncaging
Gonzales, D. T., Schuhmacher, M., Lennartz, H. M., et al. (2023) · Biophysical Journal · doi:10.1016/j.bpj.2023.11.013 · Cited by 3
Practical Identifiability in a Viscoelastic Respiratory Model for Mechanical Ventilation
Cerdeira, A. E., Lam, N. N., Hamis, S., et al. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01497-z · Cited by 3
“M , where M is the number of parameters, profile curves are developed by fixing a single parameter, θ k, over a range of 0.2–5 times its identified value in steps of 0.01 (Appendix A), while fitting the other M − 1 parameters to the measured data (Raue et al. 2009).”
InfluentialElizondo, B. R., & Saa, P. A. (2025) · ACS Synthetic Biology · doi:10.1021/acssynbio.5c00256 · Cited by 3
An Updated Reliability Generalization Meta-Analysis on the Career Adapt-Abilities Scale
Xu, K., Chen, H., & Zhang, C. (2025) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000936 · Cited by 3
Ribeiro, A. D. M., Lopes, L. F., Rocha, B. M., et al. (2025) · Water Resources Research · doi:10.1029/2024wr039536 · Cited by 3
“A parameter identifiability analysis was also carried out using the profile likelihood (PL) technique (Raue et al., 2009; Wieland et al., 2021), comparing commonly used parameter estimation approaches with the one proposed here.”
InfluentialDolat, M., Wright, A. D., Gharamaleki, S. B., et al. (2025) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2025.109537 · Cited by 3
Wang, X. (2026) · Bulletin of Mathematical Biology · doi:10.1007/s11538-026-01596-5 · Cited by 3
“Profile likelihood methods (Raue et al. 2009) provide an alternative route for assessing identifiability by quantifying confidence regions for parameters under finite data conditions.”
Levy, B., & Elveren, A. Y. (2026) · Defence and Peace Economics · doi:10.1080/10242694.2026.2624522 · Cited by 4
Yeboah, M. K., Asiedu, N. Y., & Addo, A. (2026) · Sensors · doi:10.3390/s26123948 · Cited by 3
“The logarithmic parameter transformation was appropriate because the kinetic uncertainties were multiplicative and because simultaneous biochemical effects can create practical identifiability degeneracies [28,29].”
InfluentialLinear system identifiability from single-cell data
Aalto, A., Lamoline, F., & Gonçalves, J. M. (2022) · Systems & Control Letters · doi:10.1016/j.sysconle.2022.105287 · Cited by 3
Identifiability and Parameter Estimation of Within-Host Model of HIV with Immune Response
Liyanage, Y. R., Kohan, L. M., Martcheva, M., et al. (2024) · Mathematics · doi:10.3390/math12182837 · Cited by 3
Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data
Norman, G., Wentz, J., Kolla, H., Maute, K. K., & Doostan, A. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117684 · Cited by 5
Bonamente, M., Zimmerman, D. L., & Chen, Y. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ad9b1f · Cited by 3
Villa, C., Maini, P. K., Browning, A. P., Jenner, A. L., Hamis, S., & Cassidy, T. (2025) · Journal of Mathematical Biology · doi:10.1007/s00285-025-02246-5 · Cited by 8
“For example, for a mathematical model to be uniquely parameterised it must be identifiable (Bellman and Åström 1970; Raue et al. 2009; Cassidy 2023 ).”
Structural and practical identifiability of approximate metabolic network models
Berthoumieux, S., Kahn, D., de Jong, H., et al. (2012) · IFAC Proceedings Volumes · doi:10.3182/20120711-3-be-2027.00166 · Cited by 3
Thorn, G. J., & King, J. R. (2015) · Mathematical Biosciences · doi:10.1016/j.mbs.2015.10.016 · Cited by 3
Kim, J. H., & Lee, J. M. (2018) · Bioprocess and Biosystems Engineering · doi:10.1007/s00449-018-1999-8 · Cited by 3
Experimental design for parameter estimation in steady-state linear models of metabolic networks
Frøysa, H. G., Skaug, H. J., & Alendal, G. (2019) · Mathematical Biosciences · doi:10.1016/j.mbs.2019.108291 · Cited by 3
de Cellès, M. D., Campbell, H. J., Borrow, R., Taha, M., & Opatowski, L. (2020) · BMC Medicine · doi:10.1186/s12916-020-01552-7 · Cited by 3
“estimates and to compute approximate 95% CI for each parameter [45].”
MethodImmunological heterogeneity informs estimation of the durability of vaccine protection
de Cellès, M. D., Wong, A., Guevara, L. A. B., & Rohani, P. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0070 · Cited by 2
“If the lower (upper) confidence bound equalled the lower (upper) limit of the estimation interval (0.05 – 50 years) for a given epidemiological scenario, the corresponding parameter estimates were considered practically non-identifiable for decreasing (increasing) parameter values[45].”
BackgroundMethodInfluentialEnhanced online identification of battery models exploiting data richness
Cai, C., Auger, D. J., & Perinpanayagam, S. (2023) · IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC) · doi:10.1109/esars-itec57127.2023.10114851 · Cited by 3
“In this study, “parameter identifiable” refers to structural identifiability, while “practical identifiability” is considered as part of data sensitivity [12].”
BackgroundAbout the identifiability and observability of the SIR epidemic model with quarantine
Hamelin, F., Iggidr, A., Rapaport, A., et al. (2023) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2023.10.1384 · Cited by 3
Metadata
- Authors
- Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., & Timmer, J.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Raue, A.
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2009-06-08
- Volume
- 25
- Issue
- 15
- Pages
- 1923-1929
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- OpenAlex
- W2168648059
- Cited by
- 1,442
- References
- 29
- Citations by year
- 2026: 209 · 2025: 107 · 2024: 103 · 2023: 82 · 2022: 98 · 2021: 118 · 2020: 97 · 2019: 116 · 2018: 94 · 2017: 78 · 2016: 87 · 2015: 64 · 2014: 52 · 2013: 54 · 2012: 39
- FWCI
- 10.99
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Bioinformatics (publishedVersion)
- PubMed (publishedVersion)
- OPUS (Augsburg University) (submittedVersion)
- Funders
- Deutsches Krebsforschungszentrum
- European Commission (223188, EU-FP7, FP7 HEALTH)
- Bundesministerium für Bildung und Forschung (FRISYS 0313921, 0313074D, 0313921)
- FP7 Health
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Microbial Metabolic Engineering and Bioproduction
- Keywords
- identifiability analysis, profile likelihood, parameter estimation, confidence intervals, experimental design, model reduction
- MeSH terms
- Algorithms, Models, Biological, Probability, Computational Biology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
