Bayesian analysis for Markov jump processes is a non-trivial and challenging
problem. Although exact inference is theoretically possible, it is
computationally demanding thus its applicability is limited to a small class of
problems. In this paper we describe the application of Riemann manifold MCMC
methods using an approximation to the likelihood of the Markov jump process
which is valid when the system modelled is near its thermodynamic limit. The
proposed approach is both statistically and computationally efficient while the
convergence rate and mixing of the chains allows for fast MCMC inference. The
methodology is evaluated using numerical simulations on two problems from
chemical kinetics and one from systems biology
