in our framework, we focus our discussion on the lower (up to sixth order) moments.]{}

[Our expansion is based on two successive Taylor expansions that allow us to express the CME of the moment generating function in computationally convenient form]{}; and we truncate the system by setting higher order terms in the Taylor expansions to zero. The outlined method [could]{} fit into a general framework for parameter inference based on maximum entropy distributions derived from the calculated moments. [We furthermore demonstrate that parameter sensitivity analyses may be performed naturally and efficiently in this framework: we can consider the rate of change of the moments with respect to the parameters, which also allows us to study the factors underlying cell-to-cell variability.]{} We illustrate the [general]{} method using three molecular reaction systems: a simple dimerisation reaction, which allows for a detailed investigation; Michaelis-Menten enzyme kinetics; and the p53 system, an oscillating tumour suppressor system [@Batchelor:2009hk].

Moment expansion method
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We consider a system with $N$ different molecular species $(X_1,...X_N)$ that are involved in $L$ chemical reactions with reaction rates $k_l$, $$\begin{aligned}
\underbar{s}_1X_1+...+\underbar{s}_NX_N \xrightarrow{k_l}  \bar{s}_1X_1+...+\bar{s}_NX_N,\end{aligned}$$ with $\underbar{s}_i$ and $\bar{s}_i$ the number of molecules of type $X_i$ before and after the reaction, respectively. The 