IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v26y2021i3d10.1007_s13253-021-00446-2.html
   My bibliography  Save this article

Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions

Author

Listed:
  • Baisen Liu

    (Dongbei University of Finance and Economics)

  • Liangliang Wang

    (Simon Fraser University)

  • Yunlong Nie

    (Google Inc.)

  • Jiguo Cao

    (Simon Fraser University)

Abstract

Ordinary differential equation (ODE) models are popularly used to describe complex dynamical systems. When estimating ODE parameters from noisy data, a common distribution assumption is using the Gaussian distribution. It is known that the Gaussian distribution is not robust when abnormal data exist. In this article, we develop a hierarchical semiparametric mixed-effects ODE model for longitudinal data under the Bayesian framework. For robust inference on ODE parameters, we consider a class of heavy-tailed distributions to model the random effects of ODE parameters and observations errors. An MCMC method is proposed to sample ODE parameters from the posterior distributions. Our proposed method is illustrated by studying a gene regulation experiment. Simulation studies show that our proposed method provides satisfactory results for the semiparametric mixed-effects ODE models with finite samples. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Baisen Liu & Liangliang Wang & Yunlong Nie & Jiguo Cao, 2021. "Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 428-445, September.
    • Handle: RePEc:spr:jagbes:v:26:y:2021:i:3:d:10.1007_s13253-021-00446-2
    DOI: 10.1007/s13253-021-00446-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-021-00446-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-021-00446-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. Khanin & V. Vinciotti & V. Mersinias & C. P. Smith & E. Wit, 2007. "Statistical Reconstruction of Transcription Factor Activity Using Michaelis–Menten Kinetics," Biometrics, The International Biometric Society, vol. 63(3), pages 816-823, September.
    2. Jiguo Cao & James Ramsay, 2007. "Parameter cascades and profiling in functional data analysis," Computational Statistics, Springer, vol. 22(3), pages 335-351, September.
    3. Nicolas J-B. Brunel & Quentin Clairon & Florence d'Alché-Buc, 2014. "Parametric Estimation of Ordinary Differential Equations With Orthogonality Conditions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 173-185, March.
    4. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2015. "On the selection of ordinary differential equation models with application to predator-prey dynamical models," Biometrics, The International Biometric Society, vol. 71(1), pages 131-138, March.
    5. S. Choy & A. Smith, 1997. "Hierarchical models with scale mixtures of normal distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 205-221, June.
    6. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    7. Liang, Hua & Wu, Hulin, 2008. "Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1570-1583.
    8. Yangxin Huang & Hulin Wu, 2006. "A Bayesian approach for estimating antiviral efficacy in HIV dynamic models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(2), pages 155-174.
    9. J. Guedj & R. Thiébaut & D. Commenges, 2007. "Maximum Likelihood Estimation in Dynamical Models of HIV," Biometrics, The International Biometric Society, vol. 63(4), pages 1198-1206, December.
    10. Peter Hall & Yanyuan Ma, 2014. "Quick and easy one-step parameter estimation in differential equations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 735-748, September.
    11. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    12. J. Cao & L. Wang & J. Xu, 2011. "Robust Estimation for Ordinary Differential Equation Models," Biometrics, The International Biometric Society, vol. 67(4), pages 1305-1313, December.
    13. G. J. M. Rosa & D. Gianola & C. R. Padovani, 2004. "Bayesian Longitudinal Data Analysis with Mixed Models and Thick-tailed Distributions using MCMC," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 855-873.
    14. Yunlong Nie & LiangLiang Wang & Jiguo Cao, 2017. "Estimating time‐varying directed gene regulation networks," Biometrics, The International Biometric Society, vol. 73(4), pages 1231-1242, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    2. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Hanwen Huang, 2022. "Bayesian multi‐level mixed‐effects model for influenza dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1978-1995, November.
    4. Shizhe Chen & Ali Shojaie & Daniela M. Witten, 2017. "Network Reconstruction From High-Dimensional Ordinary Differential Equations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1697-1707, October.
    5. Carey, M. & Ramsay, J.O., 2021. "Fast stable parameter estimation for linear dynamical systems," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    6. Hulin Wu & Hongqi Xue & Arun Kumar, 2012. "Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research," Biometrics, The International Biometric Society, vol. 68(2), pages 344-352, June.
    7. Zhou, Jie, 2015. "Detection of influential measurement for ordinary differential equation with application to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 324-332.
    8. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2017. "Estimating varying coefficients for partial differential equation models," Biometrics, The International Biometric Society, vol. 73(3), pages 949-959, September.
    9. Hanwen Huang & Andreas Handel & Xiao Song, 2020. "A Bayesian approach to estimate parameters of ordinary differential equation," Computational Statistics, Springer, vol. 35(3), pages 1481-1499, September.
    10. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    11. Cao, Jiguo & Ramsay, James O., 2009. "Generalized profiling estimation for global and adaptive penalized spline smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2550-2562, May.
    12. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2015. "On the selection of ordinary differential equation models with application to predator-prey dynamical models," Biometrics, The International Biometric Society, vol. 71(1), pages 131-138, March.
    13. Mu Niu & Joe Wandy & Rónán Daly & Simon Rogers & Dirk Husmeier, 2021. "R package for statistical inference in dynamical systems using kernel based gradient matching: KGode," Computational Statistics, Springer, vol. 36(1), pages 715-747, March.
    14. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    15. Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.
    16. Quentin Clairon & Chloé Pasin & Irene Balelli & Rodolphe Thiébaut & Mélanie Prague, 2024. "Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach," Computational Statistics, Springer, vol. 39(6), pages 2975-3005, September.
    17. Ying Zhu, 2021. "Phase transitions in nonparametric regressions," Papers 2112.03626, arXiv.org, revised Nov 2023.
    18. Commenges, D. & Jolly, D. & Drylewicz, J. & Putter, H. & Thiébaut, R., 2011. "Inference in HIV dynamics models via hierarchical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 446-456, January.
    19. Mu Niu & Benn Macdonald & Simon Rogers & Maurizio Filippone & Dirk Husmeier, 2018. "Statistical inference in mechanistic models: time warping for improved gradient matching," Computational Statistics, Springer, vol. 33(2), pages 1091-1123, June.
    20. Jiguo Cao & Gregor F. Fussmann & James O. Ramsay, 2008. "Estimating a Predator‐Prey Dynamical Model with the Parameter Cascades Method," Biometrics, The International Biometric Society, vol. 64(3), pages 959-967, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jagbes:v:26:y:2021:i:3:d:10.1007_s13253-021-00446-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.