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

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.

Keywords:

• Bayesian ODE-penalized B-spline
• ordinary differential equations
• parameter estimation
• penalized Gaussian mixture
• pharmacokinetics

Acknowledgements

This work started at the Université Catholique de Louvain with the financial support from the IAP Research Network P6/03 of the Belgian government (Belgian Science Policy). Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) is gratefully acknowledged.