  Inferring the parameters of ordinary differential equations (ODEs) from noisy
observations is an important problem in many scientific fields. Currently, most
parameter estimation methods that bypass numerical integration tend to rely on
basis functions or Gaussian processes to approximate the ODE solution and its
derivatives. Due to the sensitivity of the ODE solution to its derivatives,
these methods can be hindered by estimation error, especially when only sparse
time-course observations are available. We present a Bayesian collocation
framework that operates on the integrated form of the ODEs and also avoids the
expensive use of numerical solvers. Our methodology has the capability to
handle general nonlinear ODE systems. We demonstrate the accuracy of the
proposed method through simulation studies, where the estimated parameters and
recovered system trajectories are compared with other recent methods. A real
data example is also provided.
