Synthetic likelihood method for reaction network inference

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, from the stochastic data generating process, 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 the method, we apply it in two real data examples: the molecular pathway analysis with RNA-seq and the famous incidence data from 1665 plague outbreak at Eyam, England.