  This study concerns online inference (i.e., filtering) on the state of
reaction networks, conditioned on noisy and partial measurements. The
difficulty in deriving the equation that the conditional probability
distribution of the state satisfies stems from the fact that the master
equation, which governs the evolution of the reaction networks, is analytically
intractable. The linear noise approximation (LNA) technique, which is widely
used in the analysis of reaction networks, has recently been applied to develop
approximate inference. Here, we apply the projection method to derive
approximate filters, and compare them to a filter based on the LNA numerically
in their filtering performance. We also contrast the projection method with
moment-closure techniques in terms of approximating the evolution of stochastic
reaction networks.
