Bayesian reconstructions and predictions of nonlinear dynamical systems via the hybrid Monte Carlo scheme

Time series prediction is a rather difficult problem when the dynamics behind the data originates from a nonlinear system and its functional form is unknown. The hierarchical Bayesian scheme previously proposed by the authors has been shown to be reasonably sound for nontrivial real world applications. A great difficulty implementing the Hierarchical Bayesian scheme lies in the computation of posterior distributions as well as 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 the Hybrid Monte Carlo scheme, a particular class of Markov Chain Monte Carlo without the Quadratic Approximations. The scheme is tested against two concrete problems; Chaotic time series prediction, and Building air-conditioning Load Prediction. The prediction results are compared with those using the Quadratic Approximations which have been used in the previous works of the authors' group. The proposed scheme outperforms the Quadratic Approximations.