  Approximate Bayesian computation (ABC) using a sequential Monte Carlo method
provides a comprehensive platform for parameter estimation, model selection and
sensitivity analysis in differential equations. However, this method, like
other Monte Carlo methods, incurs a significant computational cost as it
requires explicit numerical integration of differential equations to carry out
inference. In this paper we propose a novel method for circumventing the
requirement of explicit integration by using derivatives of Gaussian processes
to smooth the observations from which parameters are estimated. We evaluate our
methods using synthetic data generated from model biological systems described
by ordinary and delay differential equations. Upon comparing the performance of
our method to existing ABC techniques, we demonstrate that it produces
comparably reliable parameter estimates at a significantly reduced execution
time.
