highly efficient at capturing the behaviour of stochastic systems in terms of the average and higher moments, and we provide expressions for the computational cost for different system sizes and orders of approximation. [We show how the moment expansion method can be employed to efficiently [quantify parameter sensitivity]{}.]{} Finally we investigate the effects of using too few moments on parameter estimation, and provide guidance on how to estimate if the distribution can be accurately approximated using only a few moments.'
author:
- Angelique Ale
- Paul Kirk
- 'Michael P.H. Stumpf'
title: A general moment expansion method for stochastic kinetic models
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Introduction
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Cellular behaviour is shaped by molecular process that can be described by systems of chemical reactions between different molecular species. At the macroscopic scale, the dynamics of these processes are frequently described in terms of mean concentrations of species using deterministic mass action kinetics (MAK). The deterministic solution, however, does not always capture the essential kinetics of the chemical system accurately, because it excludes stochastic effects.

The stochastic kinetics of chemical reaction systems are captured by the chemical master equation (CME), a probabilistic description of the system (also known as Kolmogorov’s forward equation) [@Gardiner2009; 