  In this work, we present an extension to the context of Stochastic Reaction
Networks (SRNs) of the forward-reverse representation introduced in "Simulation
of forward-reverse stochastic representations for conditional diffusions", a
2014 paper by Bayer and Schoenmakers. We apply this stochastic representation
in the computation of efficient approximations of expected values of
functionals of SNR bridges, i.e., SRNs conditioned to its values in the
extremes of given time-intervals. We then employ this SNR bridge-generation
technique to the statistical inference problem of approximating the reaction
propensities based on discretely observed data. To this end, we introduce a
two-phase iterative inference method in which, during phase I, we solve a set
of deterministic optimization problems where the SRNs are replaced by their
reaction-rate Ordinary Differential Equations (ODEs) approximation; then,
during phase II, we apply the Monte Carlo version of the
Expectation-Maximization (EM) algorithm starting from the phase I output. By
selecting a set of over dispersed seeds as initial points for phase I, the
output of parallel runs from our two-phase method is a cluster of approximate
maximum likelihood estimates. Our results are illustrated by numerical
examples.
