Andrew Golightly, School of Mathematics & Statistics, Newcastle University Presentation: http://mbi.osu.edu/2011/rasmaterials/AGmbi12.pdf We consider the problem of performing Bayesian inference for the rate constants governing stochastic kinetic models. As well as considering inference for the resulting Markov jump process (MJP) we consider working with a diffusion approximation obtained by matching the infinitesimal mean and variance of the MJP to the drift and diffusion coefficients of a stochastic differential equation (SDE). We sample from the posterior distribution of the model parameters given observations at discrete times via recently proposed particle MCMC methods. In the case of the diffusion approximation we increase the efficiency of the inference algorithm by exploiting the structure of the SDE. We present results from two toy examples: a Lotka-Volterra system and a simple model of prokaryotic autoregulation.