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Cited by 68Control Systems and IdentificationStatistical and numerical algorithmsAgriculture, Soil, Plant Science

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Determining the parametric structure of models

Cole, D.J., Morgan, B.J.T., Titterington, D.M.·2010·Mathematical Biosciences
DOI 10.1016/j.mbs.2010.08.004
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Abstract

In this paper we develop a comprehensive approach to determining the parametric structure of models. This involves considering whether a model is parameter redundant or not and investigating model identifiability. The approach adopted makes use of exhaustive summaries, quantities that uniquely define the model. We review and generalise previous work on evaluating the symbolic rank of an appropriate derivative matrix to detect parameter redundancy, and then develop further tools for use within this framework, based on a matrix decomposition. Complex models, where the symbolic rank is difficult to calculate, may be simplified structurally using reparameterisation and by finding a reduced-form exhaustive summary. The approach of the paper is illustrated using examples from ecology, compartment modelling and Bayes networks. This work is topical as models in the biosciences and elsewhere are becoming increasingly complex.

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Research works printed but not linked: 46

  1. Rothenberg, 1971, Identification in parametric models, Econometrica, 39, 577, 10.2307/1913267 · DOI
  2. Goodman, 1974, Exploratory latent structure analysis using both identifiable and unidentifiable models, Biometrika, 61, 215, 10.1093/biomet/61.2.215 · DOI
  3. H. Pohjanpalo, Identifiability of deterministic differential models in state space, Technical Research Centre of Finland Research Report No. 56, 1982. · DOI
  4. Shapiro, 1986, Asymptotic theory of overparameterized structural models, Journal of the American Statistical Association, 81, 142, 10.2307/2287981 · DOI
  5. Catchpole, 1997, Detecting parameter redundancy, Biometrika, 84, 187, 10.1093/biomet/84.1.187 · DOI
  6. Walter, 1982, Global approaches to identifiability testing for linear and nonlinear state space models, Mathematics and Computers in Simulation, 24, 472, 10.1016/0378-4754(82)90645-0 · DOI
  7. Catchpole, 2001, Deficiency of parameter-redundant models, Biometrika, 88, 593, 10.1093/biomet/88.2.593 · DOI
  8. Cole, 2010, A note on determining parameter redundancy in age-dependent tag return models for estimating fishing mortality, natural mortality and selectivity, JABES, 10.1007/s13253-010-0026-6 · DOI
  9. Cole, 2010, Parameter redundancy with covariates, Biometrika, 10.1093/biomet/asq041 · DOI
  10. Catchpole, 2002, Solving problems in parameter redundancy using computer algebra, Journal of Applied Statistics, 29, 625, 10.1080/02664760120108601 · DOI
  11. Cormack, 1964, Estimates of survival from the sightings of marked animals, Biometrika, 51, 429, 10.1093/biomet/51.3-4.429 · DOI
  12. Jolly, 1965, Explicit estimates from capture–recapture data with both death and immigration, Biometrika, 52, 225, 10.1093/biomet/52.1-2.225 · DOI
  13. Seber, 1965, A note on the multiple recapture census, Biometrika, 52, 249, 10.1093/biomet/52.1-2.249 · DOI
  14. Bellman, 1970, On structural identifiability, Mathematical Biosciences, 7, 329, 10.1016/0025-5564(70)90132-X · DOI · Paper page
  15. Grewal, 1976, Identifiability of linear and nonlinear dynamical systems, IEEE Transactions on Automatic Control, AC-21, 833, 10.1109/TAC.1976.1101375 · DOI
  16. Pohjanpalo, 1978, System identifiability based on the power series of the solution, Mathematical Biosciences, 41, 21, 10.1016/0025-5564(78)90063-9 · DOI · Paper page
  17. Walter, 1982, Identifiability of State Space Models, vol. 46
  18. Vajda, 1989, Similarity transformation approach to structural identifiability of nonlinear models, Mathematical Biosciences, 93, 217, 10.1016/0025-5564(89)90024-2 · DOI
  19. Chappell, 1998, A procedure for generating locally identifiable reparameterisations of unidentifiable non-linear systems by the similarity transformation approach, Mathematical Biosciences, 148, 21, 10.1016/S0025-5564(97)10004-9 · DOI
  20. Thowsen, 1978, Identifiability of dynamic systems, International Journal of Systems Science, 9, 813, 10.1080/00207727808941738 · DOI
  21. Magaria, 2001, Differential algebra methods for the study of the structural identifiability of rational function state-space models in biosciences, Mathematical Biosciences, 174, 1, 10.1016/S0025-5564(01)00079-7 · DOI · Paper page
  22. Delforge, 1985, Local identifiability of linear systems in a general input-output configuration, International Journal of Systems Science, 16, 1015, 10.1080/00207728508926729 · DOI
  23. Delforge, 1989, Relations between the main approaches to linear system identifiability: application to calculation of jacobian matrices determinants, International Journal of Systems Science, 20, 1079, 10.1080/00207728908910193 · DOI
  24. Walter, 1981, Unidentifiable compartmental models: what to do?, Mathematical Biosciences, 56, 1, 10.1016/0025-5564(81)90025-0 · DOI
  25. H.P. Wynn, N. Parkin, Sensitivity analysis and identifiability for differential equation models, in: Proceedings of 40th IEEE Conference on Decision & Control, 2001, pp. 3116–3121. · DOI
  26. A. Donzé, G. Clermont, A. Legay, C.J. Langmead, Parameter synthesis in nonlinear dynamical systems: application to systems biology, in: Proceedings of 13th Annual International Conference on Computational Molecular Biology (RECOMB), 2009, pp. 155–169. · DOI
  27. Errico, 1997, What is an adjoint model?, Bulletin of the American Meteorological Society, 78, 2577, 10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2 · DOI
  28. McNamara, 2004, Fluid control using the adjoint method, ACM Transactions on Graphics, 23, 449, 10.1145/1015706.1015744 · DOI
  29. Catchpole, 1998, Estimation in parameter redundant models, Biometrika, 85, 462, 10.1093/biomet/85.2.462 · DOI
  30. Evans, 2000, Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems, Mathematical Biosciences, 168, 137, 10.1016/S0025-5564(00)00047-X · DOI
  31. Little, 2009, Parameter identifiability and redundancy in a general class of stochastic carcinogenesis models, PLoS ONE, 4, e8520, 10.1371/journal.pone.0008520 · DOI
  32. Little, 2010, Parameter identifiability and redundancy: theoretical considerations, PLoS ONE, 5, e8915, 10.1371/journal.pone.0008915 · DOI
  33. Catchpole, 2001, On the near-singularity of models for animal recovery data, Biometrics, 57, 720, 10.1111/j.0006-341X.2001.00720.x · DOI
  34. Gimenez, 2003, Parameter redundancy in multistate capture–recapture models, Biometrical Journal, 45, 704, 10.1002/bimj.200390043 · DOI
  35. Corless, 1997, The Turing factorization of a rectangular matrix, SIGSAM Bulletin, 31, 20, 10.1145/271130.271135 · DOI
  36. Catchpole, 1996, Steps to parameter redundancy in age-dependent recovery models, Journal of the Royal Statistical Society Series B, 58, 763, 10.1111/j.2517-6161.1996.tb02114.x · DOI
  37. Shapiro, 1983, On the investigation of local identifiability: a counterexample, Psychometrika, 48, 303, 10.1007/BF02294025 · DOI
  38. C.M. Hunter, H. Caswell, Rank and redundancy of multistate mark-recapture models for seabird populations with unobservable states, in: D.L. Thomson, E.G. Cooch, M.J. Conroy (Eds.), Modelling Demographic Processes in Marked Populations: Series: Environmental and Ecological Statistics, vol. 3, 2009, pp. 797–826.
  39. Jiang, 2007, Age-dependent tag return models for estimating fishing mortality, natural mortality and selectivity, JABES, 12, 177, 10.1198/108571107X197382 · DOI
  40. Audoly, 1998, Global identifiability of linear compartmental models – A computer algebra algorithm, IEEE Transactions on Biomedical Engineering, 45, 36, 10.1109/10.650350 · DOI
  41. Dochain, 1995, Structural identifiability of biokinetic models of activated sludge respiration, Water Research, 29, 2571, 10.1016/0043-1354(95)00106-U · DOI
  42. M. Whiley, Aspects of the interface between statistics and neural networks, Ph.D Thesis, University of Glasgow, Scotland, 1999.
  43. Brooks, 2000, On the Bayesian analysis of ring-recovery data, Biometrics, 56, 951, 10.1111/j.0006-341X.2000.00951.x · DOI
  44. Catchpole, 1991, A note on Seber’s model for ring-recovery data, Biometrika, 78, 917, 10.1093/biomet/78.4.917 · DOI
  45. Garrett, 2000, Latent class model diagnosis, Biometrics, 56, 1055, 10.1111/j.0006-341X.2000.01055.x · DOI
  46. O. Gimenez, B.J.T. Morgan, S.P. Brooks, Weak identifiability in models for mark-recapture-recovery data, in: D.L. Thomson, E.G. Cooch, M.J. Conroy (Eds.), Modelling Demographic Processes in Marked Populations: Series: Environmental and Ecological Statistics, vol. 3, 2009, pp. 1057–1070.

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Metadata

Authors
Cole, D. J., Morgan, B. J. T., & Titterington, D. M.
Affiliations
  • University of Kent (GB)
  • University of Glasgow (GB)
Corresponding author
Cole, D.J.
ORCID
Venue
Mathematical Biosciences
Publisher
Elsevier BV
Published
2010-11
Volume
228
Issue
1
Pages
16-30
ISSN
0025-5564 (ISSN-L)
DOI
10.1016/j.mbs.2010.08.004
OpenAlex
W2149396711
Cited by
68
References
1
Citations by year
2026: 1 · 2025: 2 · 2024: 4 · 2023: 2 · 2022: 3 · 2021: 6 · 2020: 7 · 2019: 8 · 2018: 3 · 2017: 3 · 2016: 4 · 2015: 2 · 2014: 8 · 2013: 6 · 2012: 5
FWCI
7.43
Type
journal article
Language
en
Open access
closed
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Mathematical Biosciences (publishedVersion)
  • PubMed (publishedVersion)
  • ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) (submittedVersion)
  • Kent Academic Repository (University of Kent) (submittedVersion)
Funders
Engineering and Physical Sciences Research Council (EP/C522702/1)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
  • Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
  • Life Sciences › Agricultural and Biological Sciences › Agronomy and Crop Science › Agriculture, Soil, Plant Science
Keywords
parameter redundancy, model identifiability, matrix factorization, reparameterization, reduced-form models, compartmental model, Bayesian networks, ecological model
MeSH terms
Algorithms, Bayes Theorem, Models, Biological, Oxygen, Sewage, Models, Statistical, Likelihood Functions, Linear Models, Nonlinear Dynamics, Ecosystem, Computational Biology

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CoChat. (2026). Citation check: Determining the parametric structure of models. https://app.cochat.ai/papers/10.1016/j.mbs.2010.08.004
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Cole, D. J., Morgan, B. J. T., & Titterington, D. M. (2010). Determining the parametric structure of models. Mathematical Biosciences. https://doi.org/10.1016/j.mbs.2010.08.004