Pith. sign in

REVIEW 2 major objections 3 minor 70 references

Think before you fit: parameter identifiability, sensitivity and uncertainty in systems biology models

T0 review · 2 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Before fitting a systems biology model, check whether its parameters can be learned from the data at all—this review argues identifiability, not just fit quality, sets the limits of prediction.

desk verdict Useful review of identifiability methods for systems biology, with one false mathematical equivalence (FIM rank vs local structural identifiability) that needs correcting. read the letter →

arxiv 2508.18853 v1 pith:3WB6QRMW submitted 2025-08-26 stat.ME math.STq-bio.QMstat.APstat.TH

Simon P. Preston , Richard D. Wilkinson , Richard H. Clayton , Mike J. Chappell , Gary R. Mirams This is my paper
classification stat.MEmath.STq-bio.QMstat.APstat.TH MSC 92C4262-0262F12
keywords identifiabilitypracticalstructuralFisherinformationmatrixprofilelikelihoodsensitivityanalysissystemsbiologyparameterestimation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review argues that before fitting a systems biology model you must ask whether its parameters can be learned from the data at all, and with what precision. It distinguishes structural identifiability—learnable given infinite perfect data—from practical identifiability—learnable with acceptable precision from finite noisy data—and shows how the Fisher information matrix, profile likelihood, and synthetic-data re-inference expose both. The central warning is that weakly identifiable parameters can quietly produce good fits yet break predictions outside the calibration setting. A sympathetic reader is meant to leave with a workflow: check identifiability, then decide whether to improve the experiment, simplify the model, or add prior information. The paper makes no claim about model misspecification, which it explicitly leaves out of scope.

What carries the argument

The carrying object is the Fisher information matrix I(θ) = σ⁻²V(θ)ᵀV(θ), built from the sensitivity matrix V = dE[y]/dθ. In the linear case I = σ⁻²XᵀX is constant; its rank decides structural identifiability and its eigenvalues and eigenvectors give the directions and sizes of parameter uncertainty through the asymptotic distribution θ̂ ≈ N(θ*, I(θ*)⁻¹). The same object transfers to nonlinear models as a local approximation, and profile likelihood plus synthetic-data re-inference extend the check beyond the local quadratic picture.

What would settle it

Take a set of systems-biology ODE models, fit each to synthetic data generated from the same model, and record out-of-sample prediction error on unseen experimental conditions. If models with near-zero Fisher information eigenvalues or flat profile likelihoods regularly deliver predictions as accurate as those of identifiable models, the central warning would be contradicted. Conversely, a single well-documented case where an apparently well-identified model fails dramatically on unseen data due to parameter combinations that were unidentifiable in the training design would support it.

Watch

Extended reading notes

Core claim

The paper's central claim is that identifiability is not a technical afterthought but the property that determines the limits of inference and prediction. For a parametric model f(t, θ), identifiability is injectivity of the map θ → Pθ: different parameter values must give different distributions for the observed data. Structural identifiability asks whether θ could be recovered from infinite, noise-free data; practical identifiability asks whether finite, noisy data constrain θ enough for the intended use. In linear models the Fisher information matrix I = σ⁻²XᵀX completely answers this: rank deficiency means structural unidentifiability, and small eigenvalues mean poor practical identifiab

Load-bearing premise

The entire toolkit assumes the model is correctly specified: that some true parameter value within the model class can generate the data up to noise. If the model is misspecified, identifiability checks overstate the fidelity of calibration, and parameter estimates are biased by compromise fits.

Editorial extensions

If this is right

  • A full-rank Fisher information matrix is necessary but not sufficient for trustworthy prediction; the experimental design—time points, measured outputs, repeated measurements—determines how much information the data carry.
  • Weakly identifiable parameters can be addressed either by measuring different outputs or refining the model structure, or by adding prior knowledge and regularization.
  • Nonlinearity means identifiability must be assessed across parameter space, not once at a single estimate.
  • Models that pass identifiability checks in the training context can still fail at prediction time, so the quantity of interest should be uncertainty in the predicted output, not just uncertainty in parameters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same logic points toward automated 'identifiability gates' in model-fitting pipelines: before any parameter estimate is reported, a synthetic-data re-inference or profile-likelihood check could be run, and models failing it flagged rather than released.
  • Because the paper excludes model misspecification, its recommendations are most safely read as applying to models whose form is trusted; for real biological systems, predictive validation against unseen data remains the only complete check.
  • A testable extension: for a class of ODE models, rank models by minimum Fisher information eigenvalue and measure out-of-sample prediction error; if the ranking holds, identifiability checks double as model-selection scores.
  • For expensive simulators, emulator-based Fisher information matrices could screen parameters before committing to full Markov chain or profile-likelihood analysis.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper is a review/tutorial, not a new methods paper. It argues that structural and practical identifiability should be checked before fitting systems biology models, and that Fisher information matrix (FIM), profile likelihood, and synthetic-data re-inference checks can reveal when weakly identifiable parameters may undermine out-of-sample predictions. It defines identifiability concepts, develops linear-model intuition, then treats nonlinear models, global sensitivity analysis, emulators, and strategies for improving identifiability (experimental design, model reduction, priors). The Conclusions acknowledge that model discrepancy/misspecification is outside scope and recommend predictive validation on unseen data.

Significance. As a review, the paper's value is pedagogical synthesis: clear diagrammatic classification of identifiability concepts, an accessible linear-model derivation of the FIM, practical guidance in choosing methods by model complexity, and honest treatment of limitations. It cites recent software and examples from the authors' own cardiac modeling work. It contains no new theorems or code; its central recommendation aligns with the broad identifiability literature. If the technical overstatement described below is fixed, the paper would be a useful introduction for applied researchers.

major comments (2)
  1. [From linear to nonlinear] The sentence 'A model is locally structurally identifiable at θ if and only if det I(θ) ≠ 0' is not true for nonlinear maps. Counterexample: scalar model f(θ)=θ^3 at θ*=0. The map is globally injective, hence locally structurally identifiable, yet V(0)=0 and det I(0)=0. Therefore a zero eigenvalue of the FIM is not proof of structural unidentifiability; it can occur at identifiable parameters where the local sensitivity vanishes, with estimation then converging at a nonstandard rate. Since this criterion feeds directly into the recommended local FIM check, please replace the iff by a one-way implication (full rank of V(θ) is sufficient for local structural identifiability, not necessary), or restrict the iff to the linear case.
  2. [Practical identifiability] Eq. (5) is used to justify the FIM as a measure of practical identifiability and to state that no zero eigenvalues implies local structural identifiability. The asymptotic distribution in Eq. (5) requires, among other conditions, that V(θ*) has full column rank and that the model is correctly specified. The θ^3 counterexample shows that when V is rank-deficient at θ*, the least-squares estimator is not asymptotically normal with covariance I(θ*)^(-1); it has a cube-root-rate limit. The text should state these regularity conditions and should not claim that a full-rank FIM means parameters 'can hence be learned from y' without finite-sample caveats about the correctly-specified, large-n regime.
minor comments (3)
  1. [Figure 4] The figure contains what appear to be embedded author/editor annotation notes ('Gary: are emulators commonly differentiable for FIM?', 'Right click objects and then Edit points...', 'Spare shape!'). This is not suitable for publication and must be removed or replaced with a proper caption.
  2. [Conclusions] The caveat 'Beyond the scope of this review is model discrepancy/misspecification...' is appropriately explicit, but it is introduced only at the end. Since all the reviewed diagnostics (FIM, profile likelihood, synthetic-data checks) assume correct model specification, it would help readers to signal this limitation earlier, e.g. when practical identifiability is first defined. As written, the caveat is sensible and does not weaken the main recommendation provided the FIM issue above is corrected.
  3. [General] Small presentation issues: 'anemulator' should be 'an emulator'; 'Strike-goldd' appears with inconsistent capitalization; the label 'Practical GlobalUnidentifiability(everywhere)' in Figure 1 lacks spacing. These are cosmetic but should be cleaned.

Circularity Check

0 steps flagged · score 1.0 of 10

Review is self-contained; cited prior work is illustrative, and no prediction reduces to a fit or self-citation.

full rationale

This is a review/tutorial, not a paper that fits parameters and then predicts from them. The central recommendation—that identifiability analysis is needed before calibration—is supported by classical results (e.g., the linear-model FIM relationship, asymptotic normality of least-squares estimators) and by a broad external literature, not by the authors' own prior results. The self-citations (Whittaker et al. 2020/2022, Owen and Mirams 2025, Shuttleworth et al. 2024) appear as examples in cardiac modeling, brute-force synthetic-data checks, model reduction, and model discrepancy; none is the premise from which the main conclusions are derived. No fitted input is renamed as a prediction: the paper performs no estimation. Two flagged issues are genuine but are not circular. First, the claim 'A model is locally structurally identifiable at θ if and only if det I(θ) ≠ 0' is overstated for nonlinear models (local injectivity can hold when the sensitivity vanishes at a point, e.g. f(θ)=θ^3 at θ=0), but this is a mathematical correctness concern, not a reduction of the conclusion to its inputs. Second, the Conclusions explicitly limit the review to correctly specified models: 'Beyond the scope of this review is model discrepancy/misspecification...'; this is a scoped limitation, acknowledged by the authors, and does not make the identifiability argument circular. Overall, the derivation chain is independent of its citations, so no circular step is present; the score reflects only the presence of minor non-load-bearing self-citations.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper's central claims rest on standard statistical assumptions (asymptotic normality, additive error) and on a specific equivalence between FIM rank and local structural identifiability that is stated without proof and is not universally valid. No free parameters are fitted and no new entities are introduced.

assumptions (4)
  • domain assumption Observations are generated as y = f(theta) + epsilon with random error epsilon (Eq. 1)
    All definitions of identifiability (theta -> P_theta injective) and FIM-based practical identifiability in Sections 'Introduction' through 'From linear to nonlinear' are built on this additive-error deterministic-model assumption.
  • standard math The asymptotic distribution theta-hat ~ N(theta*, I(theta*)^-1) holds (smooth f, compact Theta, theta* interior)
    Invoked in Eq. (5) to justify using the FIM as the measure of practical identifiability; the paper notes it is an approximation for finite n.
  • domain assumption The model is correctly specified (no model discrepancy)
    The Conclusions explicitly scope out model discrepancy, so the recommended diagnostics (FIM, profile likelihood, synthetic-data checks) assume the model family contains the true data-generating mechanism.
  • ad hoc to paper Local structural identifiability is equivalent to full rank of the FIM
    The paper states 'A model is locally structurally identifiable at theta if and only if det I(theta) != 0' in Section 'From linear to nonlinear'. This is not true in general, so the paper relies on a stronger, inaccurate assumption for this equivalence.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Think before you fit: parameter identifiability, sensitivity and uncertainty in systems biology models." pith.science (2026). https://pith.science/paper/3WB6QRMW

@misc{pith2026250818853,
  author       = {Pith},
  title        = {Pith review of: Think before you fit: parameter identifiability, sensitivity and uncertainty in systems biology models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3WB6QRMW}},
  note         = {Machine review of arXiv:2508.18853}
}
read the original abstract

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural identifiability) and in practice (practical identifiability). We introduce the core ideas using linear models, highlighting how experimental design and output sensitivity shape identifiability. In nonlinear models, identifiability can vary with parameter values, motivating global and simulation-based approaches. We summarise computational methods for assessing identifiability noting that weakly identifiable parameters can undermine predictions beyond the calibration dataset. Strategies to improve identifiability include measuring different outputs, refining model structure, and adding prior knowledge. Far from a technical afterthought, identifiability determines the limits of inference and prediction. Recognising and addressing identifiability is essential for building models that are not only well-fitted to data, but also capable of delivering predictions with robust, quantifiable uncertainty.

Figures

Figures reproduced from arXiv: 2508.18853 by the authors.

Figure 1
Figure 1. A diagram of implication conditions between identifiability concepts discussed. Note [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. A visualisation of identifiability concepts for one (A-B) and two (C-H) param￾eter dimensions. In all plots, the shading indicates plausible regions for the parameter value, with lighter regions indicating higher confidence, e.g., darkest is 50% confidence regions, and lightest is 95% regions. Panels A–B: For nonlinear models, the Fisher-information matrix (FIM) provides a better description of parameter identifiabi… view at source ↗
Figure 3
Figure 3. Sensitivity depends on the parameter values in nonlinear models and predictive uncertainty is not the same as parameter uncertainty. A graph of the function f(θ) = 1 + 1 θ . We highlight how parameter uncertainty can have a nonlinear relationship with uncertainty in f(θ) (predictive uncertainty). Identifiability analysis is the study of what we can learn about θ from observing f(θ). Sensitivity analysis is the study… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: A schematic showing some techniques for assessing identifiability and how computation [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

70 extracted references · 59 canonical work pages

  1. [1]

    Pohjanpalo , title System identifiability based on the power series expansion of the solution , journal Mathematical Biosciences volume 41 ( year 1978 ) pages 21--33

    author H. Pohjanpalo , title System identifiability based on the power series expansion of the solution , journal Mathematical Biosciences volume 41 ( year 1978 ) pages 21--33 . :https://doi.org/10.1016/0025-5564(78)90063-9

    doi:10.1016/0025-5564(78)90063-9 1978

  2. [2]

    Evans , author M

    author N. Evans , author M. Chapman , author M. Chappell , author K. Godfrey , title Identifiability of uncontrolled nonlinear rational systems , journal Automatica volume 38 ( year 2002 ) pages 1799--1805 . :10.1016/S0005-1098(02)00094-8

    work page doi:10.1016/s0005-1098(02)00094-8 2002

  3. [3]

    Ljung , author T

    author L. Ljung , author T. Glad , title On global identifiability for arbitrary model parametrizations , journal Automatica volume 30 ( year 1994 ) pages 265--276 . :10.1016/0005-1098(94)90029-9

    doi:10.1016/0005-1098(94)90029-9 1994

  4. [4]

    author M. P. Saccomani , author S. Audoly , author L. D'Angiò , title Parameter identifiability of nonlinear systems: The role of initial conditions , journal Automatica volume 39 ( year 2003 ) pages 619 – 632 . :10.1016/S0005-1098(02)00302-3

    work page doi:10.1016/s0005-1098(02)00302-3 2003

  5. [5]

    Margaria , author E

    author G. Margaria , author E. Riccomagno , author M. J. Chappell , author H. P. Wynn , title Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences , journal Mathematical Biosciences volume 174 ( year 2001 ) pages 1--26 . :10.1016/S0025-5564(01)00079-7

    work page doi:10.1016/s0025-5564(01)00079-7 2001

  6. [6]

    author N. D. Evans , author H. Moyse , author D. Lowe , author D. Briggs , author R. Higgins , author D. Mitchell , author D. Zehnder , author M. J. Chappell , title Structural identifiability of surface binding reactions involving heterogeneous analyte: application to surface plasmon resonance experiments , journal Automatica volume 49 ( year 2012 ) pages 48--57

    work page 2012

  7. [7]

    author J. W. T. Yates , author N. D. Evans , author M. J. Chappell , title Structural identifiability analysis via symmetries of differential equations , journal Automatica volume 45 ( year 2009 ) pages 2585--2591

    work page 2009

  8. [8]

    Massonis , author A

    author G. Massonis , author A. F. Villaverde , title Finding and breaking lie symmetries: implications for structural identifiability and observability in biological modelling , journal Symmetry volume 12 ( year 2020 ) pages 469

    work page 2020

Show all 70 references
  1. [9]

    Anguelova , author J

    author M. Anguelova , author J. Karlsson , author M. Jirstrand , title Minimal output sets for identifiability , journal Mathematical Biosciences volume 239 ( year 2012 ) pages 139--153

    2012

  2. [10]

    Karlsson , author M

    author J. Karlsson , author M. Anguelova , author M. Jirstrand , title An efficient method for structural identifiability analysis of large dynamic systems , journal IFAC Proceedings Volumes volume 45 ( year 2012 ) pages 941--946 . :10.3182/20120711-3-BE-2027.00381, note 16th ...

    2012

  3. [11]

    Raue , author J

    author A. Raue , author J. Karlsson , author M. P. Saccomani , author M. Jirstrand , author J. Timmer , title Comparison of approaches for parameter identifiability analysis of biological systems , journal Bioinformatics volume 30 ( year 2014 ) pages 1440--1448

    2014

  4. [12]

    author A. F. Villaverde , author N. D. Evans , author M. J. Chappell , author J. R. Banga , title Input-dependent structural identifiability of nonlinear systems , journal IEEE Control Systems Letters volume 3 ( year 2018 ) pages 1--6

    2018

  5. [13]

    Massonis , author J

    author G. Massonis , author J. R. Banga , author A. F. Villaverde , title Autorepar: A method to obtain identifiable and observable reparameterizations of dynamic models with mechanistic insight , journal International Journal of Robust and Nonlinear Control volume 33 ( year 2...

    2021

  6. [14]

    Díaz-Seoane , author X

    author S. Díaz-Seoane , author X. Rey Barreiro , author A. F. Villaverde , title Strike-goldd 4.0: user-friendly, efficient analysis of structural identifiability and observability , journal Bioinformatics volume 39 ( year 2023 ) pages btac748 . :10.1093/bioinformatics/btac748

    2023 doi

  7. [15]

    Meshkat , author C

    author N. Meshkat , author C. E.-z. Kuo , author J. DiStefano III , title On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and combos: A novel web implementation , journal PLoS ONE volume 9 ( year 2014 ) pages e110261

    2014

  8. [16]

    Dong , author C

    author R. Dong , author C. Goodbrake , author H. Harrington , author P. G. , title Differential elimination for dynamical models via projections with applications to structural identifiability , journal SIAM Journal on Applied Algebra and Geometry volume 7 ( year 2023 ) pages 194--235

    2023

  9. [17]

    Heinrich , author M

    author M. Heinrich , author M. Rosenblatt , author F.-G. Wieland , author H. Stigter , author J. Timmer , title On structural and practical identifiability: Current status and update of results , journal Current Opinion in Systems Biology ( year 2025 ) pages 100546

    2025

  10. [18]

    Renardy , author D

    author M. Renardy , author D. Kirschner , author M. Eisenberg , title Structural identifiability analysis of age-structured pde epidemic models , journal Journal of Mathematical Biology volume 84 ( year 2022 ) pages 9

    2022

  11. [19]

    author A. P. Browning , author M. Ta s c a , author C. Falc \'o , author R. E. Baker , title Structural identifiability analysis of linear reaction--advection--diffusion processes in mathematical biology , journal Proceedings of the Royal Society A volume 480 ( year 2024 ) pag...

    2024

  12. [20]

    Salmaniw , author A

    author Y. Salmaniw , author A. P. Browning , title Structural identifiability of linear-in-parameter parabolic pdes through auxiliary elliptic operators , journal Journal of Mathematical Biology volume 91 ( year 2025 ) pages 1--31

    2025

  13. [21]

    author H. M. Byrne , author H. A. Harrington , author A. Ovchinnikov , author G. Pogudin , author H. Rahkooy , author P. Soto , title Algebraic identifiability of partial differential equation models , journal Nonlinearity volume 38 ( year 2025 ) pages 025022

    2025

  14. [22]

    Liu , author K

    author Y. Liu , author K. Suh , author P. K. Maini , author D. J. Cohen , author R. E. Baker , title Parameter identifiability and model selection for partial differential equation models of cell invasion , journal Journal of the Royal Society Interface volume 21 ( year 2024 )...

    2024

  15. [23]

    author A. P. Browning , author M. J. Chappell , author H. Rahkooy , author T. E. Loman , author R. E. Baker , title Exact identifiability analysis for a class of partially observed near-linear stochastic differential equation models , journal arXiv volume 2503.19241 ( year 2025 )

    2025

  16. [24]

    author D. M. Bates , author D. G. Watts , title Nonlinear regression analysis and its applications , volume volume 2 , publisher Wiley New York , year 1988

    1988

  17. [25]

    author G. A. F. Seber , author C. J. Wild , title Nonlinear Regression Analysis and Its Applications , publisher John Wiley & Sons , address Nashville, TN , year 1989

    1989

  18. [26]

    author R. N. Gutenkunst , author J. J. Waterfall , author F. P. Casey , author K. S. Brown , author C. R. Myers , author J. P. Sethna , title Universally sloppy parameter sensitivities in systems biology models , journal PLoS computational biology volume 3 ( year 2007 ) pages e189

    2007

  19. [27]

    author D. G. Whittaker , author M. Clerx , author C. L. Lei , author D. J. Christini , author G. R. Mirams , title Calibration of ionic and cellular cardiac electrophysiology models , journal Wiley Interdisciplinary Reviews: Systems Biology and Medicine volume 12 ( year 2020 )...

    2020

  20. [28]

    author I. Sobol , title Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates , journal Mathematics and Computers in Simulation volume 55 ( year 2001 ) pages 271--280 . :10.1016/S0378-4754(00)00270-6

    2001 doi

  21. [29]

    Saltelli , author P

    author A. Saltelli , author P. Annoni , author I. Azzini , author F. Campolongo , author M. Ratto , author S. Tarantola , title Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index , journal Computer Physics Communications v...

    2010 doi

  22. [30]

    author M. D. Morris , title Factorial sampling plans for preliminary computational experiments , journal Technometrics volume 33 ( year 1991 ) pages 161--174 . :10.1080/00401706.1991.10484804

    1991

  23. [31]

    author A. B. Owen , title Sobol' indices and S hapley value , journal SIAM/ASA Journal on Uncertainty Quantification volume 2 ( year 2014 ) pages 245--251 . :10.1137/130936233

    2014 doi

  24. [32]

    Homma , author A

    author T. Homma , author A. Saltelli , title Importance measures in global sensitivity analysis of nonlinear models , journal Reliability Engineering & System Safety volume 52 ( year 1996 ) pages 1--17

    1996

  25. [33]

    author R. B. Gramacy , title Surrogates: Gaussian process modeling, design, and optimization for the applied sciences , publisher Chapman and Hall/CRC , year 2020

    2020

  26. [34]

    Gerritsma , author J.-B

    author M. Gerritsma , author J.-B. Van Der Steen , author P. Vos , author G. Karniadakis , title Time-dependent generalized polynomial chaos , journal Journal of Computational Physics volume 229 ( year 2010 ) pages 8333--8363 . :10.1016/j.jcp.2010.07.020

    2010 doi

  27. [35]

    Kreutz , author A

    author C. Kreutz , author A. Raue , author D. Kaschek , author J. Timmer , title Profile likelihood in systems biology , journal The FEBS Journal volume 280 ( year 2013 ) pages 2564--2571

    2013

  28. [36]

    Wieland , author A

    author F.-G. Wieland , author A. L. Hauber , author M. Rosenblatt , author C. T \"o nsing , author J. Timmer , title On structural and practical identifiability , journal Current Opinion in Systems Biology volume 25 ( year 2021 ) pages 60--69

    2021

  29. [37]

    Venzon , author S

    author D. Venzon , author S. Moolgavkar , title A method for computing profile-likelihood-based confidence intervals , journal Journal of the Royal Statistical Society: Series C (Applied Statistics) volume 37 ( year 1988 ) pages 87--94 . :10.2307/2347496

    1988 doi

  30. [38]

    author D. V. Raman , author J. Anderson , author A. Papachristodoulou , title Delineating parameter unidentifiabilities in complex models , journal Physical Review E volume 95 ( year 2017 ) pages 032314 . :10.1103/PhysRevE.95.032314

    2017 doi

  31. [39]

    author M. J. Owen , author G. R. Mirams , title Ionbench: a benchmark of optimisation strategies for mathematical models of ion channel currents , journal bioRxiv ( year 2025 ) pages 2025--01 . :10.1101/2025.01.31.635876

    2025 doi

  32. [40]

    Siekmann , author J

    author I. Siekmann , author J. Sneyd , author E. J. Crampin , title MCMC can detect nonidentifiable models , journal Biophysical Journal volume 103 ( year 2012 ) pages 2275--2286

    2012

  33. [41]

    author K. E. Hines , author T. R. Middendorf , author R. W. Aldrich , title Determination of parameter identifiability in nonlinear biophysical models: A bayesian approach , journal Journal of General Physiology volume 143 ( year 2014 ) pages 401--416

    2014

  34. [42]

    Vernon , author M

    author I. Vernon , author M. Goldstein , author R. Bower , title Galaxy formation: Bayesian history matching for the observable universe , journal Statistical science ( year 2014 ) pages 81--90

    2014

  35. [43]

    author P. S. Craig , author M. Goldstein , author A. H. Seheult , author J. A. Smith , title Pressure matching for hydrocarbon reservoirs: a case study in the use of bayes linear strategies for large computer experiments , in: booktitle Case Studies in Bayesian Statistics: Vol...

    1997

  36. [44]

    Csill \'e ry , author M

    author K. Csill \'e ry , author M. G. Blum , author O. E. Gaggiotti , author O. Fran c ois , title Approximate bayesian computation (abc) in practice , journal Trends in ecology & evolution volume 25 ( year 2010 ) pages 410--418

    2010

  37. [45]

    author R. D. Wilkinson , title Approximate bayesian computation (abc) gives exact results under the assumption of model error , journal Statistical applications in genetics and molecular biology volume 12 ( year 2013 ) pages 129--141

    2013

  38. [46]

    author R. D. Wilkinson , author C. W. Lanyon , title An introduction to the calibration of computer models , journal arXiv preprint arXiv:2310.09214 ( year 2023 )

    2023 arXiv

  39. [47]

    author J. F. Apgar , author D. K. Witmer , author F. M. White , author B. Tidor , title Sloppy models, parameter uncertainty, and the role of experimental design , journal Molecular BioSystems volume 6 ( year 2010 ) pages 1890--1900

    2010

  40. [48]

    author J. E. Jeong , author Q. Zhuang , author M. K. Transtrum , author E. Zhou , author P. Qiu , title Experimental design and model reduction in systems biology , journal Quantitative Biology volume 6 ( year 2018 ) pages 287--306

    2018

  41. [49]

    Joubert , author J

    author D. Joubert , author J. Stigter , author J. Molenaar , title Determining minimal output sets that ensure structural identifiability , journal PLoS One volume 13 ( year 2018 ) pages e0207334

    2018

  42. [50]

    author G. C. Goodwin , author R. L. Payne , title Dynamic System Identification: Experiment Design and Data Analysis , volume volume 136 of series Mathematics in Science and Engineering , publisher Academic Press , year 1977

    1977

  43. [51]

    Thomaseth , author C

    author K. Thomaseth , author C. Cobelli , title Generalized sensitivity functions in physiological system identification , journal Annals of Biomedical Engineering volume 27 ( year 1999 ) pages 607--616

    1999

  44. [52]

    Fink , author D

    author M. Fink , author D. Noble , title Markov models for ion channels: versatility versus identifiability and speed , journal Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 367 ( year 2009 ) pages 2161--2179

    2009

  45. [53]

    author S. Pant , title Information sensitivity functions to assess parameter information gain and identifiability of dynamical systems , journal Journal of The Royal Society Interface volume 15 ( year 2018 ) pages 20170871 . :10.1098/rsif.2017.0871

    2018

  46. [54]

    author J. L. M \"u nch , author R. Schmauder , author F. Paul , author M. Habeck , title Using bayesian priors to overcome non-identifiablility issues in hidden markov models , journal bioRxiv ( year 2025 ). :10.1101/2024.04.20.590387

    2025 doi

  47. [55]

    Semochkina , author C

    author D. Semochkina , author C. D. Walsh , title Incorporating additional evidence as prior information to resolve non-identifiability in bayesian disease model calibration: A tutorial , journal Statistics in Medicine volume 44 ( year 2025 ) pages e70039

    2025

  48. [56]

    Biktasheva , author R

    author I. Biktasheva , author R. Simitev , author R. Suckley , author V. Biktashev , title Asymptotic properties of mathematical models of excitability , journal Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 364 ( yea...

    2006

  49. [57]

    author M. K. Transtrum , author P. Qiu , title Model reduction by manifold boundaries , journal Physical Review Letters volume 113 ( year 2014 ) pages 098701 . :10.1103/physrevlett.113.098701

    2014 doi

  50. [58]

    author D. G. Whittaker , author J. Wang , author J. G. Shuttleworth , author R. Venkateshappa , author J. M. Kemp , author T. W. Claydon , author G. R. Mirams , title Ion channel model reduction using manifold boundaries , journal Journal of the Royal Society Interface volume ...

    2022

  51. [59]

    Creswell , author K

    author R. Creswell , author K. M. Shepherd , author B. Lambert , author G. R. Mirams , author C. L. Lei , author S. Tavener , author M. Robinson , author D. J. Gavaghan , title Understanding the impact of numerical solvers on inference for differential equation models , journa...

    2024

  52. [60]

    Cobelli , author J

    author C. Cobelli , author J. J. Distefano 3rd , title Parameter and structural identifiability concepts and ambiguities: a critical review and analysis , journal American Journal of Physiology-Regulatory, Integrative and Comparative Physiology volume 239 ( year 1980 ) pages R7--R24

    1980

  53. [61]

    author C. C. Margossian , title A review of automatic differentiation and its efficient implementation , journal Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery volume 9 ( year 2019 ) pages e1305

    2019

  54. [62]

    Sapienza , author J

    author F. Sapienza , author J. Bolibar , author F. Sch \"a fer , author B. Groenke , author A. Pal , author V. Boussange , author P. Heimbach , author G. Hooker , author F. P \'e rez , author P.-O. Persson , author C. Rackauckas , title Differentiable programming for different...

    2024

  55. [63]

    author M. J. Colebank , title Assessing parameter identifiability of a hemodynamics PDE model using spectral surrogates and dimension reduction , journal arXiv preprint arXiv:2506.04538 ( year 2025 )

    2025 arXiv

  56. [64]

    White , author M

    author A. White , author M. Tolman , author H. D. Thames , author H. R. Withers , author K. A. Mason , author M. K. Transtrum , title The limitations of model-based experimental design and parameter estimation in sloppy systems , journal PLoS Computational Biology volume 12 ( ...

    2016

  57. [65]

    Tuo , author C

    author R. Tuo , author C. J. Wu , title Efficient calibration for imperfect computer models , journal Ann. Statist. volume 43 ( year 2015 ) pages 2331--2352

    2015

  58. [66]

    author C. L. Lei , author S. Ghosh , author D. G. Whittaker , author Y. Aboelkassem , author K. A. Beattie , author C. D. Cantwell , author T. Delhaas , author C. Houston , author G. M. Novaes , author A. V. Panfilov , et al., title Considering discrepancy when calibrating a m...

    2020

  59. [67]

    author J. G. Shuttleworth , author C. L. Lei , author D. G. Whittaker , author M. J. Windley , author A. P. Hill , author S. P. Preston , author G. R. Mirams , title Empirical quantification of predictive uncertainty due to model discrepancy by training with an ensemble of exp...

    2024

  60. [68]

    author M. C. Kennedy , author A. O'Hagan , title Bayesian calibration of computer models , journal Journal of the Royal Statistical Society: Series B (Statistical Methodology) volume 63 ( year 2001 ) pages 425--464

    2001

  61. [69]

    Brynjarsd \'o ttir , author A

    author J. Brynjarsd \'o ttir , author A. O'Hagan , title Learning about physical parameters: The importance of model discrepancy , journal Inverse Problems volume 30 ( year 2014 ) pages 114007

    2014

  62. [70]

    Plumlee , title Bayesian calibration of inexact computer models , journal Journal of the American Statistical Association volume 112 ( year 2017 ) pages 1274--1285

    author M. Plumlee , title Bayesian calibration of inexact computer models , journal Journal of the American Statistical Association volume 112 ( year 2017 ) pages 1274--1285

    2017

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.