We have previously shown that Bayesian statistics together with Markov chain Monte Carlo (MCMC) procedures can be applied to hidden Markov model (HMM) analysis of synthetic, unfiltered single channel currents buried in white noise. However, experimental data are filtered and contaminated with coloured noise. Venkataramanan et al. (1998) and Qin et al. (1998) have shown that the forward-backward procedure for maximizing the HMM likelihood can be used with higher order Markov chains to take these effects into account. Our MCMC approach has been extended to incorporate the effects of filtering and colouration. Preliminary results suggest that when these effects are taken into account, the MCMC methods require less computational effort than the forward-backward maximization procedures. In addition, inferences are based on the support of a distribution rather than on simple point estimates. These methods have been tested using synthetic data and are currently being applied to experimental data.