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Approximate Inference for Stochastic Reaction processes

We discuss the problem of statistical inference for Markov jump processes modeling biochemical reactions. Using a variational formulation of exact inference we derive two different approximations. A weak noise approach within a diffusion approximation is relevant when the number of individuals of a given species is rather large. On the other hand a mean field approximation takes the discreteness of the number of individuals into account but neglects correlations.