  Stochastic reaction network models arise in intracellular chemical reactions,
epidemiological models and other population process models, and are a class of
continuous time Markov chains which have the nonnegative integer lattice as
state space. We consider the problem of estimating the conditional probability
distribution of a stochastic reaction network given exact partial state
observations in time snapshots. We propose a particle filtering method called
the targeting method. Our approach takes into account that the reaction counts
in between two observation snapshots satisfy linear constraints and also uses
inhomogeneous Poisson processes as proposals for the reaction counts to
facilitate exact interpolation. We provide rigorous analysis as well as
numerical examples to illustrate our method and compare it with other
alternatives.
