Parameter Estimation of Kinetic Rates in Stochastic Reaction Networks by the EM Method

Gillespie's algorithm serves to simulate a network of stochastic reactions with given initial quantities and kinetic rate constants.  In this paper we consider the estimation of the kinetic rate constants of the reactions based on a set of discrete observations generated by Gillespie's algorithm. In particular, we present an Expectation Maximisation (EM) method to perform maximum likelihood estimation of the rate constants.  Applicability of the method is tested on a simple reaction network.