IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v41y2014i12p2709-2726.html
   My bibliography  Save this article

Bayesian penalized smoothing approaches in models specified using differential equations with unknown error distributions

Author

Listed:
  • Jonathan Jaeger
  • Philippe Lambert

Abstract

A full Bayesian approach based on ordinary differential equation (ODE)-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some state functions involved in systems of affine differential equations. Simulations inspired by pharmacokinetic (PK) studies show that the proposed method provides comparable results to the method based on the standard ODE-penalized B-spline approach (i.e. with the Gaussian error distribution assumption) and outperforms the standard ODE-penalized B-splines when the distribution is not Gaussian. This methodology is illustrated on a PK data set.

Suggested Citation

  • Jonathan Jaeger & Philippe Lambert, 2014. "Bayesian penalized smoothing approaches in models specified using differential equations with unknown error distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2709-2726, December.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:12:p:2709-2726
    DOI: 10.1080/02664763.2014.927839
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2014.927839
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2014.927839?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. Lambert, Philippe & Eilers, Paul H.C., 2009. "Bayesian density estimation from grouped continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1388-1399, February.
    2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    3. Komarek, Arnost & Lesaffre, Emmanuel, 2008. "Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 523-533, June.
    4. Jaeger, Jonathan & Lambert, Philippe, 2013. "Bayesian P-spline estimation in hierarchical models specified by systems of affine differential equations," LIDAM Reprints ISBA 2013016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Lambert, Philippe, 2011. "Nonparametric additive location-scale models for interval censored data," LIDAM Reprints ISBA 2011032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    7. Lambert, Philippe, 2007. "Archimedean copula estimation using Bayesian splines smoothing techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6307-6320, August.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gianluca Frasso & Jonathan Jaeger & Philippe Lambert, 2016. "Parameter estimation and inference in dynamic systems described by linear partial differential equations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 259-287, July.

    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. Jaeger, Jonathan & Lambert, Philippe, 2012. "Bayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions," LIDAM Discussion Papers ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Gianluca Frasso & Jonathan Jaeger & Philippe Lambert, 2016. "Parameter estimation and inference in dynamic systems described by linear partial differential equations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 259-287, July.
    3. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.
    4. JAEGER, Jonathan & LAMBERT, Philippe, 2011. "Bayesian generalized profiling estimation in hierarchical linear dynamic systems," LIDAM Discussion Papers ISBA 2011001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Panagiotis Papastamoulis & George Iliopoulos, 2013. "On the Convergence Rate of Random Permutation Sampler and ECR Algorithm in Missing Data Models," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 293-304, June.
    6. Komárek, Arnost, 2009. "A new R package for Bayesian estimation of multivariate normal mixtures allowing for selection of the number of components and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3932-3947, October.
    7. You, Na & Dai, Hongsheng & Wang, Xueqin & Yu, Qingyun, 2024. "Sequential estimation for mixture of regression models for heterogeneous population," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    8. José Dias & Jeroen Vermunt, 2008. "A bootstrap-based aggregate classifier for model-based clustering," Computational Statistics, Springer, vol. 23(4), pages 643-659, October.
    9. Juarez, Miguel A. & Steel, Mark F. J., 2006. "Model-based Clustering of non-Gaussian Panel Data," MPRA Paper 880, University Library of Munich, Germany.
    10. Arima, Serena & Basset, Alberto & Jona Lasinio, Giovanna & Pollice, Alessio & Rosati, Ilaria, 2013. "A hierarchical Bayesian model for the ecological status classification of lagoons," Ecological Modelling, Elsevier, vol. 263(C), pages 187-195.
    11. Rodríguez, Carlos E. & Núñez-Antonio, Gabriel & Escarela, Gabriel, 2020. "A Bayesian mixture model for clustering circular data," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    12. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    13. Philippe Lambert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 284-286, August.
    14. Ungolo, Francesco & Kleinow, Torsten & Macdonald, Angus S., 2020. "A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 68-84.
    15. Park, Byung-Jung & Zhang, Yunlong & Lord, Dominique, 2010. "Bayesian mixture modeling approach to account for heterogeneity in speed data," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 662-673, June.
    16. Kozumi, Hideo, 2004. "Posterior analysis of latent competing risk models by parallel tempering," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 441-458, June.
    17. Moya, Blake & Walker, Stephen G., 2024. "Full uncertainty analysis for Bayesian nonparametric mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    18. Jia-Chiun Pan & Chih-Min Liu & Hai-Gwo Hwu & Guan-Hua Huang, 2015. "Allocation Variable-Based Probabilistic Algorithm to Deal with Label Switching Problem in Bayesian Mixture Models," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-23, October.
    19. Weber, Anett & Steiner, Winfried J., 2021. "Modeling price response from retail sales: An empirical comparison of models with different representations of heterogeneity," European Journal of Operational Research, Elsevier, vol. 294(3), pages 843-859.
    20. Roy Costilla & Ivy Liu & Richard Arnold & Daniel Fernández, 2019. "Bayesian model-based clustering for longitudinal ordinal data," Computational Statistics, Springer, vol. 34(3), pages 1015-1038, September.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:41:y:2014:i:12:p:2709-2726. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.