  Approximate Bayesian computation methods can be used to evaluate posterior
distributions without having to calculate likelihoods. In this paper we discuss
and apply an approximate Bayesian computation (ABC) method based on sequential
Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC
SMC gives information about the inferability of parameters and model
sensitivity to changes in parameters, and tends to perform better than other
ABC approaches. The algorithm is applied to several well known biological
systems, for which parameters and their credible intervals are inferred.
Moreover, we develop ABC SMC as a tool for model selection; given a range of
different mathematical descriptions, ABC SMC is able to choose the best model
using the standard Bayesian model selection apparatus.
