  We consider the problem of efficiently performing simulation and inference
for stochastic kinetic models. Whilst it is possible to work directly with the
resulting Markov jump process, computational cost can be prohibitive for
networks of realistic size and complexity. In this paper, we consider an
inference scheme based on a novel hybrid simulator that classifies reactions as
either "fast" or "slow" with fast reactions evolving as a continuous Markov
process whilst the remaining slow reaction occurrences are modelled through a
Markov jump process with time dependent hazards. A linear noise approximation
(LNA) of fast reaction dynamics is employed and slow reaction events are
captured by exploiting the ability to solve the stochastic differential
equation driving the LNA. This simulation procedure is used as a proposal
mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for
the model parameters. We apply the scheme to a simple application and compare
the output with an existing hybrid approach and also a scheme for performing
inference for the underlying discrete stochastic model.
