  Approaches to Bayesian inference for problems with intractable likelihoods
have become increasingly important in recent years. Approximate Bayesian
computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are
popular methods for tackling inference in these scenarios but such techniques
are computationally expensive. In this paper we compare the two approaches to
inference, with a particular focus on parameter inference for stochastic
kinetic models, widely used in systems biology. Discrete time transition
kernels for models of this type are intractable for all but the most trivial
systems yet forward simulation is usually straightforward. We discuss the
relative merits and drawbacks of each approach whilst considering the
computational cost implications and efficiency of these techniques. In order to
explore the properties of each approach we examine a range of observation
regimes using two example models. We use a Lotka--Volterra predator prey model
to explore the impact of full or partial species observations using various
time course observations under the assumption of known and unknown measurement
error. Further investigation into the impact of observation error is then made
using a Schl\"ogl system, a test case which exhibits bi-modal state stability
in some regions of parameter space.
