and

Summary. This paper is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intra-cellular processes. The under-lying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behaviour and the model is identified using equispaced time course data. The estima-tion framework involves the introduction ofm−1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic auto-regulatory gene network