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

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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