Reconstructions and Predictions of Nonlinear Dynamical Systems Weighted by Model Marginal Likelihoods

A Hierarchical Bayesian Approach

Abstract

A hierarchical Bayesian approach is formulated for nonlinear time series prediction problems with neural nets. The proposed scheme consists of several steps :
(i) Formulae for posterior distributions of parameters, hyper parameters as well as models via Bayes formula.
(ii) Derivation of predictive distributions of future values taking into account model marginal likelihoods.
(iii) Using several drastic approximations for computing predictive mean of time series incorporating model marginal likelihoods.
The proposed scheme is tested against two examples; (A) Time series data generated by noisy chaotic dynamical system, and (B) Building air-conditioning load prediction problem. The proposed scheme outperforms the algorithm previously used by the authors.