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Stochastic reaction network models arise in intracellular chemical reactions,epidemiological models and other population process models, and are a class ofcontinuous time Markov chains which have the nonnegative integer lattice asstate space. We consider the problem of estimating the conditional probabilitydistribution of a stochastic reaction network given exact partial stateobservations in time snapshots. We propose a particle filtering method calledthe targeting method. Our approach takes into account that the reaction countsin between two observation snapshots satisfy linear constraints and also usesinhomogeneous Poisson processes as proposals for the reaction counts tofacilitate exact interpolation. We provide rigorous analysis as well asnumerical examples to illustrate our method and compare it with otheralternatives.

Stochastic Filtering of Reaction Networks Partially Observed in Time Snapshots