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In this work, we present an extension to the context of Stochastic ReactionNetworks (SRNs) of the forward-reverse representation introduced in "Simulationof forward-reverse stochastic representations for conditional diffusions", a2014 paper by Bayer and Schoenmakers. We apply this stochastic representationin the computation of efficient approximations of expected values offunctionals of SNR bridges, i.e., SRNs conditioned to its values in theextremes of given time-intervals. We then employ this SNR bridge-generationtechnique to the statistical inference problem of approximating the reactionpropensities based on discretely observed data. To this end, we introduce atwo-phase iterative inference method in which, during phase I, we solve a setof deterministic optimization problems where the SRNs are replaced by theirreaction-rate Ordinary Differential Equations (ODEs) approximation; then,during phase II, we apply the Monte Carlo version of theExpectation-Maximization (EM) algorithm starting from the phase I output. Byselecting a set of over dispersed seeds as initial points for phase I, theoutput of parallel runs from our two-phase method is a cluster of approximatemaximum likelihood estimates. Our results are illustrated by numericalexamples.

An Efficient Forward-Reverse Expectation-Maximization Algorithm for Statistical Inference in Stochastic Reaction Networks