Bayesian estimation of time-varying parameters in ordinary differential equation models with noisy time-varying covariates

Ordinary differential equations (ODEs) are important mathematical models in applied sciences to describe dynamic processes. The parameters involved in the models usually have specific meanings, and hence need to be estimated from the observed data. In applications, the parameters may change with time, which are called time-varying parameters. In this paper, we propose a Bayesian penalized B-spline method to estimate the time-varying parameters and initial values in ODEs. Simulation studies show that this method is more efficient than the two-stage local polynomial method. Furthermore, we introduce the DIC model selection criterion to determine the number of knots of B-splines.