Bayesian penalized smoothing approaches in models specified using differential equations with unknown error distributions |
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Authors: | Jonathan Jaeger Philippe Lambert |
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Affiliation: | 1. Méthodes Quantitatives en Sciences Sociales, Université de Liège, Liège, Belgium;2. Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium |
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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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Keywords: | Bayesian ODE-penalized B-spline ordinary differential equations parameter estimation penalized Gaussian mixture pharmacokinetics |
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