  We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse
engineering the topological structure of stochastic reaction networks, a
notoriously challenging problem that is relevant in many modern areas of
research, like discovering gene regulatory networks or analyzing epidemic
spread. The method relies on projecting the original time series trajectories
onto information rich summary statistics and constructing the appropriate
synthetic likelihood function to estimate reaction rates. The resulting
estimates are consistent in the large volume limit and are obtained without
employing complicated tuning strategies and expensive resampling as typically
used by likelihood-free MCMC and approximate Bayesian methods. To illustrate
run time improvements that can be achieved with our approach, we present a
simulation study on inferring rates in a stochastic dynamical system arising
from a density dependent Markov jump process. We then apply the method to two
real data examples: the RNA-seq data from zebrafish experiment and the
incidence data from 1665 plague outbreak at Eyam, England.
