  Stochastic kinetic models (SKMs) are increasingly used to account for the
inherent stochasticity exhibited by interacting populations of species in areas
such as epidemiology, population ecology and systems biology. Species numbers
are modelled using a continuous-time stochastic process, and, depending on the
application area of interest, this will typically take the form of a Markov
jump process or an It\^o diffusion process. Widespread use of these models is
typically precluded by their computational complexity. In particular,
performing exact fully Bayesian inference in either modelling framework is
challenging due to the intractability of the observed data likelihood,
necessitating the use of computationally intensive techniques such as particle
Markov chain Monte Carlo (particle MCMC). It is proposed to increase the
computational and statistical efficiency of this approach by leveraging the
tractability of an inexpensive surrogate derived directly from either the jump
or diffusion process. The surrogate is used in three ways: in the design of a
gradient-based parameter proposal, to construct an appropriate bridge and in
the first stage of a delayed-acceptance step. The resulting approach, which
exactly targets the posterior of interest, offers substantial gains in
efficiency over a standard particle MCMC implementation.
