Markov chain Monte Carlo algorithms for SDE parameter estimation

This chapter considers stochastic differential equations for Systems Biology models derived from the Chemical Langevin Equation (CLE). After outlining the derivation of such models, Bayesian inference for the parameters is considered, based on state-of-the-art Markov chain Monte Carlo algorithms. Starting with a basic scheme for models observed perfectly, but discretely in time, problems with standard schemes and their solutions are discussed. Extensions of these schemes to partial observation and observations subject to measurement error are also considered. Finally, the techniques are demonstrated in the context of a simple stochastic kinetic model of a genetic regulatory network.