  In recent years dynamical modelling has been provided with a range of
breakthrough methods to perform exact Bayesian inference. However it is often
computationally unfeasible to apply exact statistical methodologies in the
context of large datasets and complex models. This paper considers a nonlinear
stochastic differential equation model observed with correlated measurement
errors and an application to protein folding modelling. An Approximate Bayesian
Computation (ABC) MCMC algorithm is suggested to allow inference for model
parameters within reasonable time constraints. The ABC algorithm uses
simulations of "subsamples" from the assumed data generating model as well as a
so-called "early rejection" strategy to speed up computations in the ABC-MCMC
sampler. Using a considerate amount of subsamples does not seem to degrade the
quality of the inferential results for the considered applications. A
simulation study is conducted to compare our strategy with exact Bayesian
inference, the latter resulting two orders of magnitude slower than ABC-MCMC
for the considered setup. Finally the ABC algorithm is applied to a large size
protein data. The suggested methodology is fairly general and not limited to
the exemplified model and data.
