  Stochastic systems in biology often exhibit substantial variability within
and between cells. This variability, as well as having dramatic functional
consequences, provides information about the underlying details of the system's
behaviour. It is often desirable to infer properties of the parameters
governing such systems given experimental observations of the mean and variance
of observed quantities. In some circumstances, analytic forms for the
likelihood of these observations allow very efficient inference: we present
these forms and demonstrate their usage. When likelihood functions are
unavailable or difficult to calculate, we show that an implementation of
approximate Bayesian computation (ABC) is a powerful tool for parametric
inference in these systems. However, the calculations required to apply ABC to
these systems can also be computationally expensive, relying on repeated
stochastic simulations. We propose an ABC approach that cheaply eliminates
unimportant regions of parameter space, by addressing computationally simple
mean behaviour before explicitly simulating the more computationally demanding
variance behaviour. We show that this approach leads to a substantial increase
in speed when applied to synthetic and experimental datasets.
