the linear noise approximation (LNA), the CME is approximated by taking into account the mean (the first moment), and the variance and covariance (second central moments) of the distribution, whereby the second central moments are decoupled form the mean[@Komorowski2009; @Komorowski2010; @Pahle2012; @Wallace2012]. This is valid in the limit of large volumes and molecule numbers, or when the system consists of first-order reactions only.

For smaller systems and more complex reactions, a number of different approaches have been developed that aim to [capture]{} the temporal changes in coupled moments. These expansions can be performed in terms of the moments or the central moments about the mean; the conversion from molecule numbers can be kept implicit in the rate parameters or made more explicit from the outset. the expansion is done in terms of central moments up to third order for first and second order rate equations, and up to second order for general rate equations. In a recent paper [@Grima2012] it was shown that expansion up to three moments tends to deliver more accurate results than expansion up to only second order; in particular the variances are improved by going to higher moments. While the MFK, 2MA and 3MA approaches include 