  This paper addresses the problem of statistical inference for latent
continuous-time stochastic processes, which is often intractable, particularly
for discrete state space processes described by Markov jump processes. To
overcome this issue, we propose a new tractable inference scheme based on an
entropic matching framework that can be embedded into the well-known
expectation propagation algorithm. We demonstrate the effectiveness of our
method by providing closed-form results for a simple family of approximate
distributions and apply it to the general class of chemical reaction networks,
which are a crucial tool for modeling in systems biology. Moreover, we derive
closed form expressions for point estimation of the underlying parameters using
an approximate expectation maximization procedure. We evaluate the performance
of our method on various chemical reaction network instantiations, including a
stochastic Lotka-Voltera example, and discuss its limitations and potential for
future improvements. Our proposed approach provides a promising direction for
addressing complex continuous-time Bayesian inference problems.
