Bayesian MCMC nonlinear time series prediction: predictive mean and error bar

When nonlinear dynamical system is behind time series data, predictions are rather difficult. Hierarchical Bayesian scheme previously proposed by the authors has been shown to be reasonably sound. A great difficulty implementing the hierarchical Bayesian scheme lies in the computation of predictive distributions for which quadratic approximations have been used so far. This paper attempts to compute predictive mean and error bar for nonlinear time series prediction problems via MCMC (Markov Chain Monte Carlo) without quadratic approximations. The scheme is tested against time series generated by (Chaotic) Rossler system.