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
35 Own interpretation · 14 Own result · 6 No full text of the sources · 6 No basis given · 1 Partly supported · 1 Sources not found · 1 Not checked yet · 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
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- 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)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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 > )]:
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably 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
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
“Species concentrations are modeled in nanometer.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
“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
Cited by
Sorted by citations
Items 1,001–1,100 of 1,414
Kim, K.-H., Sibanda, N., Arnold, R., & A’mar, T. (2024) · Canadian Journal of Fisheries and Aquatic Sciences · doi:10.1139/cjfas-2023-0358 · Cited by 3
Mechanistic modelling - a BOLD response to the fMRI information loss problem
Lundengård, K. (2017) · Linköping University medical dissertations · doi:10.3384/diss.diva-142870 · Cited by 4
“This type of plot is called a profile likelihood plot, and is the result of a profile likelihood analysis [78][79].”
BackgroundGlobal optimization using Gaussian processes to estimate biological parameters from image data
Barac, D., Multerer, M., & Iber, D. (2018) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2018.12.002 · Cited by 2
Pedretscher, B., Kaltenbacher, B., & Pfeiler, O. (2019) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2019.06.020 · Cited by 2
Building New Models: Rethinking and Revising ODE Model Assumptions
Hurtado, P. J. (2020) · Foundations for undergraduate research in mathematics · doi:10.1007/978-3-030-33645-5_1 · Cited by 2
Stochastic Methods for Inferring States of Cell Migration
Allen, R. J., Welch, C. M., Pankow, N., et al. (2020) · Frontiers in Physiology · doi:10.3389/fphys.2020.00822 · Cited by 2
“To assess the accuracy of our parameter estimates we used confidence-interval profiling [18].”
MethodИгоревна, К. О., & Andornaya, D. V. (2021) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2092/1/012012 · Cited by 2
Mathematical modelling of cell cycle and telomere dynamics
Hirt, B. V. (2013) · Nottingham ePrints (University of Nottingham) · Cited by 2
Functional redundancy in the NF-\kappa B signalling pathwayPreprint
Włodarczyk, M., Lipniacki, T., & Komorowski, M. (2013) · arXiv (Cornell University) · Cited by 2
Bianconi, F., Antonini, C., Tomassoni, L., & Valigi, P. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/197400 · Cited by 2
Overstall, A. M., Woods, D. C., & Parker, B. M. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1509.04099 · Cited by 2
“See Raue et al. (2009) and Chkrebtii et al. (2015) for analyses of these data.”
MethodIdentifiability and experimental design in perturbation studiesPreprint
Groß, T., & Blüthgen, N. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.02.03.931816 · Cited by 2
“…apply different heuristics, such as network sparsity, to justify parameter regularisation (Gardner et al. , 2003; Bonneau et al. , 2006; Tegner et al. , 2003), or numerically analyse identifiability through an exploration of the parameter space using a profile likelihood approach (Raue et al. , 2009).”
MethodStructural identifiability of large systems biology models
Joubert, D. (2020) · doi:10.18174/507603 · Cited by 2
Rosenbaum, B., & Fronhofer, E. A. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.09.13.460028 · Cited by 2
“Practical identifiability, which is based both on the model and data quality (Raue et al., 2009), was 366 validated for several widely-used population models with respect to the different statistical models used here.”
BackgroundMethodA Steady-State Algebraic Model for the Time Course of Covalent Enzyme InhibitionPreprint
Kuzmič, P. (2020) · ChemRxiv · doi:10.26434/chemrxiv.12445394.v2 · Cited by 2
Adaptation to host cell environment during experimental evolution of Zika virusPreprint
Grass, V., Hardy, E., Kobert, K., et al. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.12.28.424577 · Cited by 2
A time and single-cell resolved model of hematopoiesisPreprint
Kuciński, I., Campos, J., Barile, M., Severi, F., Bohin, N., Moreira, P. N., Allen, L., Lawson, H., Haltalli, M. L. R., Kinston, S., et al. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.09.07.506735 · Cited by 2
Inferring delays in partially observed gene regulatory networksPreprint
Hong, H., Cortez, M. J., Cheng, Y., et al. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.11.27.518074 · Cited by 2
Examining the Impact of Forcing Function Inputs on Structural IdentifiabilityPreprint
Conrad, J., & Eisenberg, M. C. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4889721 · Cited by 2
Mapping effective connectivity
Reyes, R. G., & Valdes-Sosa, P. A. (2024) · Elsevier eBooks · doi:10.1016/b978-0-12-820480-1.00184-4 · Cited by 2
MIDDoE: An MBDoE Python package for model identification, discrimination, and calibration
Tabrizi, S. Z. B., Barbera, E., da Silva, W. R. L., & Bezzo, F. (2025) · Digital Chemical Engineering · doi:10.1016/j.dche.2025.100276 · Cited by 2
Apiyo, D.-N., Mouton, J., Louw, C., Sampson, S. L., & Louw, T. M. (2021) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2021.110921 · Cited by 1
Karlsson, M., Simonsson, C., Dahlström, N., et al. (2023) · PLoS ONE · doi:10.1371/journal.pone.0279168 · Cited by 1
“Identifiability of model parameters was investigated using the profile likelihood approach [16, 17].”
MethodA simple model for the analysis of epidemics based on hospitalization data
Leisman, K. P., Park, S., Simpson, S., & Rapti, Z. (2025) · Mathematical Biosciences · doi:10.1016/j.mbs.2025.109380 · Cited by 1
Stewart, W. C., Jayaprakash, C., & Das, J. (2025) · Entropy · doi:10.3390/e27030274 · Cited by 1
“…an important step towards building mechanistic biological models, but the task of estimating model parameters from experimental data is challenging for a variety of reasons [4–6], especially when the number of distinct proteins measured in experiments is smaller than the number of model parameters.”
Identifiability Analysis of a Mathematical Model for the First Wave of COVID-19 in Türkiye
Akman, T. (2025) · Bitlis Eren Üniversitesi Fen Bilimleri Dergisi · doi:10.17798/bitlisfen.1602308 · Cited by 1
“We use the standard incidence and exclude isolated individuals, as motivated by the work [21], in the disease transmission state.”
Parameter Optimization for a Neurotransmission Recovery Model
Ernst, A., Bankowski, A., Jusyte, M., Okunola, T., Petrov, T., Walter, A. M., & Winkelmann, S. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01486-2 · Cited by 2
“A 5.2 or (Raue et al. 2009).”
InfluentialA Statistical Approach to Latent Dynamic Modeling with Differential Equations
Hackenberg, M., Pechmann, A., Kreutz, C., Kirschner, J., & Binder, H. (2025) · The American Statistician · doi:10.1080/00031305.2025.2539999 · Cited by 4
“…estimate ODE parameters from an observed time series in systems modeling (Liang and Wu 2008; Gábor and Banga 2015; Ramsay and Hooker 2017), for example, using maximum likelihood estimation and uncertainty quantification via the profile likelihood (Raue et al. 2009; Kreutz, Raue, and Tim-mer 2012).”
Self-citationOn the predictive power of food commodity futures prices in forecasting inflation
Agarwal, A., Ewald, C., Zhang, S., et al. (2025) · Quantitative Finance · doi:10.1080/14697688.2025.2536611 · Cited by 1
“This phenomenon could be largely attributed to the substantial proportion of food expenditure in the consumption patterns of low-income households, wherein increases in food prices swiftly translate into overall inflation rates (Raue et al. 2009).”
Mechanistic modeling of mitosis: Insights from three collaborative case studies
Chen, J., & Cimini, D. (2025) · Seminars in Cell and Developmental Biology · doi:10.1016/j.semcdb.2025.103643 · Cited by 2
Opportunities in multiscale modeling of mosquito-borne flaviviruses
Zitzmann, C., Adia, N. A. B., Shah, P. S., et al. (2025) · Biosystems · doi:10.1016/j.biosystems.2025.105593 · Cited by 1
Efficient data collection for establishing practical identifiability via active learning
Liu, X., Wanika, L., Chappell, M. J., & Branke, J. (2025) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2025.10.058 · Cited by 1
“This section provides a brief introduction to the principles of uncertainty sampling in active learning as well as practical identifiability analysis using the profile likelihood approach.”
Laudenschlager, S., Chauhan, D., Chaudhuri, N. R., Mascio, C. E., Udassi, J. P., Frank, B. S., Romanowicz, J., Loke, Y., Kheyfets, V. O., & Moghari, M. H. (2025) · Frontiers in Pediatrics · doi:10.3389/fped.2025.1698653 · Cited by 3
R-index: A robust metric for IVIM parameter estimation on clinical MRI scanners
Dai, Y., Jia, X., Liao, Y., et al. (2025) · Magnetic Resonance Imaging · doi:10.1016/j.mri.2025.110560 · Cited by 1
“The profile likelihood method perturbs one parameter at a time while holding others fixed to study local curvature of the cost function (38) , and asymptotic methods offer analytical approximations of local variability through likelihood function expansion (39) .”
Zeilfelder, A., Vanlier, J., Mölders, C., Kastl, P., Helm, B., de Lara, S. B., Möcklinghoff, T., Leonidou, N., Holstein, E., Vlasov, A., et al. (2025) · Cell Systems · doi:10.1016/j.cels.2025.101431 · Cited by 1
Self-citationOptimal experimental design for parameter estimation in the presence of observation noise
Qi, J., & Baker, R. E. (2025) · Mathematical Biosciences · doi:10.1016/j.mbs.2025.109571 · Cited by 1
“The practical identifiability of a parameter can be determined by examining the shape and width of the profile likelihood function [26].”
Quantitative Modeling of IgG N-Glycosylation Profiles from Population Data
Kutumova, E. O., Mandrik, N., Sharipov, R., Pučić‐Baković, M., Rapčan, B., Aulchenko, Y. S., Lauc, G., & Kolpakov, F. (2025) · International Journal of Molecular Sciences · doi:10.3390/ijms262311495 · Cited by 2
“Parameter estimation employed a cellular genetic algorithm [62] available in BioUML, which also integrates identifiability analysis [54,55] and Sobol global sensitivity analysis [56].”
Huang, Y., & Ali, S. E. O. (2025) · Journal of Radiation Research and Applied Sciences · doi:10.1016/j.jrras.2025.102104 · Cited by 1
Zugaj, D., & Nekka, F. (2025) · Journal of Pharmacokinetics and Pharmacodynamics · doi:10.1007/s10928-025-10009-4 · Cited by 1
Modelling ion channels with a view towards identifiability
Siekmann, I. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01558-3 · Cited by 1
“Alternatively, profile likelihood approaches have been applied to a wide range of models to assess identifiability (Bates and Watts 1988; Raue et al. 2009; Kreutz et al. 2012, 2013; Simpson and Maclaren 2023; Ciocanel et al. 2024; Plank and Simpson 2024) although, to the best of our knowledge, they…”
Thiel, J., Žličar, M., Steinseifer, U., Kirn, B., & Neidlin, M. (2025) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2025.111371 · Cited by 1
“Calibrating complex, multi-parameter LPMs with deterministic approaches is challenging because solutions are often non-unique due to highly nonlinear relationships between model parameters and outputs, resulting in parameter non-identifiability [22 – 24].”
Range, J., Bommarius, A. S., & Pleiss, J. (2026) · ACS Catalysis · doi:10.1021/acscatal.6c02553 · Cited by 1
Co-design of crop monitoring-modeling systems via identifiability analysis
Poudel, P., Welch, S. M., Alderman, P. D., & Lin, X. (2025) · Agricultural Systems · doi:10.1016/j.agsy.2025.104613 · Cited by 2
Kosmidis, K., Markopoulos, G., & Revithiadou, A. (2025) · Applied Sciences · doi:10.3390/app16010374 · Cited by 1
Fernandes, L. D. C., Bernard, D., Pérès, F., et al. (2026) · Biosystems · doi:10.1016/j.biosystems.2025.105686 · Cited by 1
Fractional-order modelling of cancer cell population dynamics affected by radiation
Sarma, B., Dutta, H., & Das, U. (2026) · Computational Biology and Chemistry · doi:10.1016/j.compbiolchem.2026.108924 · Cited by 1
Reliable machine learning initialization methods for the calibration of Dynamic Energy Budget models
Oliveira, D. F., Marques, G. M., Santos, F., Pecquerie, L., Sousa, J. M. C., & Domingos, T. (2026) · Ecological Informatics · doi:10.1016/j.ecoinf.2026.103624 · Cited by 1
Fast identification of model parameters for fluid bed granulation ensuring low uncertainty
Schulze, M., Maus, M., Höfling, M. J., & Dosta, M. (2026) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2026.02.021 · Cited by 1
Sheng, S., & Zheng, X. (2026) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2026.114272 · Cited by 1
Kahiya, E. T., Smutný, T., Smutná, L., Tebbens, J. D., Pávek, P., & Bernhauerová, V. (2026) · Bulletin of Mathematical Biology · doi:10.1007/s11538-026-01619-1 · Cited by 1
“Nevertheless, structural identifiability does not guarantee practical identifiability (Raue et al. 2009; Wanika et al. 2024).”
Chen, M., Li, J., Li, Y., Yang, L., Zhou, C., Yang, Y., Li, W., Chen, Y., Liu, G. L., & Hu, W. (2026) · Analytical Chemistry · doi:10.1021/acs.analchem.5c07575 · Cited by 1
HAMMANI, M. E., Douiri, S. M., Harraki, I. E., et al. (2026) · Bulletin of Mathematical Biology · doi:10.1007/s11538-026-01643-1 · Cited by 1
“Thesecorrelations and identifiability challenges motivate Bayesian inference meth-ods computing full posterior distributions rather than point estimates, and profile likelihood analysis (Raue et al. 2009) to identify structural non-identifiabilities.”
Kroll, P., Deng, T., Sousa, L. M., Garg, V., Piccione, P. M., Marchal, S., Gavi, E., & Bradley, M. S. A. (2026) · International Journal of Pharmaceutics · doi:10.1016/j.ijpharm.2026.126888 · Cited by 1
Afedzi, A. E. K., Tangpromphan, P., Kamonpatana, P., & Parakulsuksatid, P. (2026) · Bioresource Technology · doi:10.1016/j.biortech.2026.134705 · Cited by 1
Timed batch inputs unlock substantially higher yields for enzymatic cascades
Jakštaitė, ., Zhou, T., Nelissen, F. H. T., Huck, W. T. S., & van Sluijs, B. (2026) · Nature Chemistry · doi:10.1038/s41557-026-02138-1 · Cited by 1
Gupta, A., & Chouhan, U. (2026) · Nonlinear Dynamics · doi:10.1007/s11071-026-12674-7 · Cited by 1
Beyond static biomarkers: systems biology and AI for decoding cancer dynamics
Dutta, S., & Goli, A. (2026) · Frontiers in Systems Biology · doi:10.3389/fsysb.2026.1855016 · Cited by 3
“Before fitting ODE or SDE models to sparse clinical series, investigators should verify structural identifiability (Villaverde et al., 2016), assess practical identifiability (Raue et al., 2009), and determine whether the sampling schedule is informative.”
Signature-Based Time-Series Analysis for System Identification: Methods That Offer Unique Benefits
Danai, K. (2015) · IEEE Control Systems · doi:10.1109/mcs.2015.2449687 · Cited by 1
“Identifiability can be analyzed at three different levels: 1) structural or a priori identifiability, based solely on the model, to detect redundancy in the parametrization of the model outputs [29], 2) input/output or posterior identifiability, based on the simulated outputs, to account for the level of excitation pr…”
BackgroundComputing enclosures for uncertain biochemical systems
August, E., & Koeppl, H. (2012) · IET Systems Biology · doi:10.1049/iet-syb.2011.0091 · Cited by 1
Models of HPV as an Infectious Disease and as an Etiological Agent of Cancer.
Brouwer, A. F. (2015) · Cited by 1
Mansell, E. J., Docherty, P. D., Chase, J. G., et al. (2015) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2015.10.120 · Cited by 1
“These methods determine when the data quantity and quality is insufficient for the size of a model, resulting in mutual interference of two or more parameters (Docherty et al., 2011, Raue et al., 2009, Saccomani, 2013).”
BackgroundMethodIdentifiability Analysis of Wall Decay Coefficients in Water Distribution Water Quality Model
Pasha, M. F. K. (2013) · World Environmental and Water Resources Congress (EWRI) · doi:10.1061/9780784412947.072 · Cited by 1
Othman, N. A., Docherty, P. D., Jamaludin, U. K., et al. (2012) · IEEE-EMBS Conference on Biomedical Engineering and Sciences · doi:10.1109/iecbes.2012.6498161 · Cited by 1
“Although the theoretical identifiability of these terms is assured [18], the practical identifiability is not robust due to the similar structural model role [19, 20].”
BackgroundCardiovascular regulation in response to multiple hemorrhages: analysis and parameter estimation
Ciocanel, M.-V., Docken, S. S., Gasper, R. E., Dean, C., Carlson, B. E., & Olufsen, M. S. (2018) · Biological Cybernetics · doi:10.1007/s00422-018-0781-y · Cited by 1
Quantitative assessment of extracellular IL-1 regulation
Ponce, L. F., García‐Martínez, K., & León, K. (2019) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2019.110113 · Cited by 1
Network Modulation in Neuropsychiatric Disorders Using the Virtual Brain
Protzner, A. B., An, S., & Jirsa, V. (2021) · Springer eBooks · doi:10.1007/978-3-030-59797-9_8 · Cited by 2
Yang, R., Jiang, C., & Shao, Y. (2022) · Bulletin of Mathematical Biology · doi:10.1007/s11538-022-01056-w · Cited by 1
“…function was designed to be optimized by the Matlab Genetic Algorithm toolbox ‘ga.’ To estimate the distance between the true values and the candidates, a first-order moment closure method (Fisher 1922; Froehlich et al. 2016; Raue et al. 2009, 2013) was implemented in the objective function design.”
MethodProfile Likelihood for Hierarchical Models Using Data Doubling
Lele, S. R. (2023) · Entropy · doi:10.3390/e25091262 · Cited by 1
SI-M/O: Swarm Intelligence-based Modeling and Optimization of complex synthesis reaction processes
Wu, M., Caprio, U. D., Elmaz, F., et al. (2023) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2023.108431 · Cited by 1
Choo, J., Jung, Y., Jo, H., et al. (2024) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2024.103670 · Cited by 1
Validation of a Multi-Strain HIV Within-Host Model with AIDS Clinical Studies
Tuncer, N., Ghods, K., Sreejithkumar, V., et al. (2024) · Mathematics · doi:10.3390/math12162583 · Cited by 1
“These methods are profile likelihood [27], Monte Carlo simulations [19,28,29], and the Fisher Information Matrix (FIM) or Correlation Matrix [30–32].”
MethodArezzo, M. F., Guagnano, G., & Vitale, D. (2025) · AStA Advances in Statistical Analysis · doi:10.1007/s10182-025-00524-7 · Cited by 1
“To this end, we performed a parameter identifiability analysis using an approach based on likelihood profiling (Raue et al. 2009).”
Core, L. D., & Mirams, G. R. (2025) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2024.0224 · Cited by 1
“However, even with structural identifiability in place, practical non-identifiability can still arise when we have poor parameter estimates due to limited amounts or quality of data [52].”
InfluentialRobust process design for the bioproduction of β-carotene in green microalgae
Flassig, R., Fachet, M., Rihko‐Struckmann, L., & Sundmacher, K. (2015) · Computer-aided chemical engineering/Computer aided chemical engineering · doi:10.1016/b978-0-444-63576-1.50047-9 · Cited by 1
Parameter identifiability analysis of power system transient models based on profile likelihood
Chen, R., Sun, H., Wu, W., Hu, Y., & Zhang, B. (2014) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm.2014.6939242 · Cited by 1
“The current work is inspired by a profile likelihood based identifiability analysis method presented in [22].”
BackgroundMethodStatistics for Model Calibration
Kreutz, C., Raue, A., & Timmer, J. (2015) · Contributions in mathematical and computational sciences · doi:10.1007/978-3-319-23321-5_14 · Cited by 1
Self-citationThe Non-Invasive Liver Biopsy : Determining Hepatic Function in Diffuse and Focal LiverDisease
Forsgren, M. F. (2017) · Linköping University medical dissertations · doi:10.3384/diss.diva-136545 · Cited by 1
Markov-Chain Monte-Carlo methods and non-identifiabilities
Müller, C. A., Weysser, F., Mrziglod, T., et al. (2018) · Monte Carlo Methods and Applications · doi:10.1515/mcma-2018-0018 · Cited by 1
Hroß, S., Theis, F. J., Sixt, M., & Hasenauer, J. (2018) · Journal of The Royal Society Interface · doi:10.1098/rsif.2018.0600 · Cited by 1
A systems toxicology paracetamol overdose framework: accounting for high-risk individuals
Mason, C. L., Leedale, J., Tasoulis, S. K., Jarman, I. H., & Webb, S. D. (2019) · Computational Toxicology · doi:10.1016/j.comtox.2019.100103 · Cited by 1
Transforming Data Across Environments Despite Structural Non-Identifiability
Singhal, V., & Murray, R. M. (2019) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2019.8814953 · Cited by 1
“In biological applications for example, this situation tends to be common due to a limited number of measurements and a large number of state variables [4].”
BackgroundSchmitt, T., & Ritter, B. (2020) · Technischen Universität Darmstadt · doi:10.25534/tuprints-00011713 · Cited by 1
Louw, C., van Schalkwyk, E. J., Conradie, R., Louw, R. P., Engelbrecht, Y., Storbeck, K., Swart, A. C., van Niekerk, D. D., Snoep, J. L., & Swart, P. (2021) · Molecular and Cellular Endocrinology · doi:10.1016/j.mce.2021.111194 · Cited by 2
Deep Hidden Physics Modeling of Cell Signaling Networks
Seeger, M., Longden, J., Klipp, E., et al. (2021) · Current Genomics · doi:10.2174/1389202922666210614131236 · Cited by 1
Inference on COVID-19 Epidemiological Parameters Using Bayesian Survival Analysis
Bardelli, C. (2021) · Entropy · doi:10.3390/e23101262 · Cited by 1
“Furthermore, the estimation of recovery times of COVID-19 is also useful to address the nonidentifiability problem [10]: in the SIR model [11] and all its extensions (SEIR [12], SIRD [13], etc.”
MethodModeling Ebola Virus Infection
(2019) · Elsevier eBooks · doi:10.1016/b978-0-12-813052-0.00016-6 · Cited by 1
Automatic generation of RC models using IoT data from commercial buildings
Xiao, Z., & Xiao, F. (2023) · Building Simulation Conference proceedings · doi:10.26868/25222708.2023.1727 · Cited by 1
“If the structure is overly complex, it may lead to parameter redundancy and unreliable parameter estimation based on measured data (Raue et al., 2009).”
BackgroundA projection and a variational regularization method for sparse inverse problems
Offtermatt, J. (2012) · OPUS Publication Server of the University of Stuttgart (University of Stuttgart) · doi:10.18419/opus-5066 · Cited by 1
de Lomana, A. L. G. (2010) · Repositori digital de la UPF (Universitat Pompeu Fabra) · Cited by 1
Graciano, J. E. A. (2016) · doi:10.11606/t.3.2016.tde-12072016-094348 · Cited by 1
Olsen, C. H., Tran, H. T., Ottesen, J. T., et al. (2013) · NCSU Libraries Repository (North Carolina State University Libraries) · Cited by 1
Stochastic nonlinear model for somatic cell population dynamics during ovarian follicle activationPreprint
Clément, F., Robin, F., & Yvinec, R. (2019) · arXiv (Cornell University) · Cited by 1
Campbell, D. A., & Lele, S. R. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1305.3299 · Cited by 1
Optimizing drug infusion schedules towards personalized cancer chronotherapyPreprint
Hill, R. J. W., Innominato, P. F., Lévi, F. A., et al. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/688606 · Cited by 1
“Next, 448 likelihood profiles of parameters of the reduced models were derived following the 449 procedure outlined in [39].”
MethodGuidelines for benchmarking of optimization approaches for fitting mathematical modelsPreprint
Kreutz, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.03427 · Cited by 1
Self-citationMathematical Modeling of the Quorum Sensing in Vibrio harveyi
Torres-Cerda, C. E. (2019) · Revista Mexicana de Ingeniería Biomédica · doi:10.17488/rmib.40.1.8 · Cited by 1
“Briefly, the approach consists on defining a set of values for each parameter, centered at its optimized value, and re-optimize the remaining parameters minimizing the SSWR [7].”
InfluentialLang, P. F., Shin, S., & Zavala, V. M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.02597 · Cited by 1
Adaptation to host cell environment during experimental evolution of Zika virusPreprint
Grass, V., Hardy, E., Kobert, K., et al. (2021) · Research Square · doi:10.21203/rs.3.rs-492894/v1 · Cited by 1
Richardson, A., Ruffin, R., & Iboi, E. (2021) · medRxiv · doi:10.1101/2021.04.08.21255156 · Cited by 1
“The intersection points between the threshold and the profile likelihood curve at given parameter values result to the bounds of the 95% confidence interval [31].”
BackgroundInterpretability of Epidemiological Models : The Curse of Non-IdentifiabilityPreprint
Deva, A., Shingi, S., Tiwari, A., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2104.14821 · Cited by 1
“We consider a parameter-wise loss function, called the profile-likelihood (PL) of θi (Raue et al., 2009), defined as where θ−i = θ \ θi denotes the complementary set of parameters.”
BackgroundMethodInfluential
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
