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Stochastic systems in biology often exhibit substantial variability withinand between cells. This variability, as well as having dramatic functionalconsequences, provides information about the underlying details of the system'sbehaviour. It is often desirable to infer properties of the parametersgoverning such systems given experimental observations of the mean and varianceof observed quantities. In some circumstances, analytic forms for thelikelihood of these observations allow very efficient inference: we presentthese forms and demonstrate their usage. When likelihood functions areunavailable or difficult to calculate, we show that an implementation ofapproximate Bayesian computation (ABC) is a powerful tool for parametricinference in these systems. However, the calculations required to apply ABC tothese systems can also be computationally expensive, relying on repeatedstochastic simulations. We propose an ABC approach that cheaply eliminatesunimportant regions of parameter space, by addressing computationally simplemean behaviour before explicitly simulating the more computationally demandingvariance behaviour. We show that this approach leads to a substantial increasein speed when applied to synthetic and experimental datasets.

Efficient parametric inference for stochastic biological systems with measured variability