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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 30 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 30
Number of page(s) 25
DOI https://doi.org/10.1051/cocv/2024019
Published online 12 April 2024
  1. N.M. Laird and J.H. Ware, Random-effects models for longitudinal data. Biometrics 38 (1982) 963–974. [CrossRef] [PubMed] [Google Scholar]
  2. M. Lavielle, Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools. CRC Press (2014). [CrossRef] [Google Scholar]
  3. G. Verbeke, Linear mixed models for longitudinal data, in Linear Mixed Models in Practice. Springer (1997) 63–153. [Google Scholar]
  4. J.C. Pinheiro and D.M. Bates, Approximations to the log-likelihood function in the nonlinear mixed-effects model. J. Computat. Graph. Stat. 4 (1995) 12–35. [CrossRef] [Google Scholar]
  5. E. Kuhn and M. Lavielle, Maximum likelihood estimation in nonlinear mixed effects models. Computat. Stat. Data Anal. 49 (2005) 1020–1038. [CrossRef] [Google Scholar]
  6. M. Prague, D. Commenges, J. Guedj, J. Drylewicz and R. Thiébaut, NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations. Comput. Methods Programs Biomed. 111 (2013) 447–458. [CrossRef] [Google Scholar]
  7. H. Wu, Statistical methods for HIV dynamic studies in aids clinical trials. Stat. Methods Med. Res. 14 (2005) 171–192. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  8. M.J. Denwood, Runjags: a R package providing interface utilities, model templates, parallel computing methods and additional distributions for MCMC models in JAGS. J. Stat. Softw. 71 (2016) 1–25. [CrossRef] [Google Scholar]
  9. B. Carpenter, A. Gelman, M.D. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. Brubaker, J. Guo, P. Li and A. Riddell, Stan: a probabilistic programming language. J. Stat. Softw. 76 (2017) 2017. [CrossRef] [Google Scholar]
  10. S.B. Duffull, C.M.J. Kirkpatrick, B. Green and N.H.G. Holford, Analysis of population pharmacokinetic data using NONMEM and WinBUGS. J. Biopharm. Stat. 15 (2004) 53–73. [CrossRef] [Google Scholar]
  11. X. Liu and Y. Wang, Comparing the performance of FOCE and different expectation-maximization methods in handling complex population physiologically-based pharmacokinetic models. J. Pharmacokinet. Pharmacodyn. 43 (2016) 359–370. [CrossRef] [PubMed] [Google Scholar]
  12. E.L. Plan, A. Maloney, F. Mentré, M.O. Karlsson and J. Bertrand. Performance comparison of various maximum likelihood nonlinear mixed-effects estimation methods for dose–response models. AAPS J. 14 (2012) 420–432. [CrossRef] [Google Scholar]
  13. E. Grenier, V. Louvet and P. Vigneaux, Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE. ESAIM: Math. Model. Numer. Anal. 48 (2014) 1303–1329. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. A. Collin, M. Prague and P. Moireau, Estimation for dynamical systems using a population-based Kalman Filter—applications in computational biology. Math. Action 11 (2022) 213–242. [CrossRef] [Google Scholar]
  15. P. Moireau, D. Chapelle and P. Le Tallec, Joint state and parameter estimation for distributed mechanical systems. Comput. Methods Appl. Mech. Eng. 1987 (2008) 659–677. [CrossRef] [Google Scholar]
  16. P. Moireau and D. Chapelle, Reduced-order unscented Kalman filtering with application to parameter identification in large-dimensional systems. ESAIM: Control Optim. Calc. Var. 17 (2011) 380–405. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  17. R. Bellman, Dynamic programming and Lagrange multipliers. Proc. Natl. Acad. Sci. U.S.A. 42 (1956) 767. [CrossRef] [PubMed] [Google Scholar]
  18. D. Luenberger, Determining the State of a Linear with Observers of Low Dynamic Order. Ph.D. thesis, Stanford University (1963). [Google Scholar]
  19. D. Pham, Stochastic methods for sequential data assimilation in strongly nonlinear systems. Monthly Weather Rev. 129 (2001) 1194–1207. [CrossRef] [Google Scholar]
  20. D.T. Pham, J. Verron and C. M. Roubaud, A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Mar. Syst. 16 (1998) 323–340. [CrossRef] [Google Scholar]
  21. D. Simon, Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches. Wiley-Interscience (2006). [Google Scholar]
  22. K. Law, A. Stuart and K. Zygalakis, Data assimilation: a mathematical introduction, Vol. 62 of Texts in Applied Mathematics. Springer, Cham (2015). [Google Scholar]
  23. S. Julier and J. Uhlmann, A new extension of the Kalman filter to nonlinear systems, in Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 1997. [Google Scholar]
  24. A. Collin, B.P. Hejblum, C. Vignals, L. Lehot, R. Thiébaut, P. Moireau and M. Prague, Using a population-based Kalman estimator to model the COVID-19 epidemic in France: estimating associations between disease transmission and non-pharmaceutical interventions. Annabelle Collin, Boris P. Hejblum, Carole Vignals, Laurent Lehot, Rodolphe Thiébaut, Philippe Moireau and Mélanie Prague. Int. J. Biostat. (2022) https://doi.org/10.1515/ijb-2022-0087. [Google Scholar]
  25. A. Collin, D. Chapelle and P. Moireau, A Luenberger observer for reaction-diffusion models with front position data. J. Computat. Phys. 300 (2015) 288–307. [CrossRef] [Google Scholar]
  26. T. Michel, J. Fehrenbach, V. Lobjois, J. Laurent, A. Gomes, T. Colin and C. Poignard, Mathematical modeling of the proliferation gradient in multicellular tumor spheroids. J. Theoret. Biol. 458 (2018) 133–147. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Collin, H. Bruhier, J. Kolosnjaj, M. Golzio, M.-P. Rols and C. Poignard, Spatial mechanistic modeling for prediction of 3D multicellular spheroids behavior upon exposure to high intensity pulsed electric fields. AIMS Bioeng. 9 (2022) 102–122. [CrossRef] [Google Scholar]
  28. C. Vaghi, A. Rodallec, R. Fanciullino, J. Ciccolini, J.P. Mochel, M. Mastri, C. Poignard, J.M. Ebos and S. Benzekry, Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS Computat. Biol. 16 (2020) e1007178. [CrossRef] [Google Scholar]

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