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.
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