Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Reconstructions and Predictions of Nonlinear Dynamical Systems Weighted by Model Marginal Likelihoods
A Hierarchical Bayesian Approach
Motoki SAITOTsuyoshi ENOMOTOTakashi MATSUMOTO
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2002 Volume 15 Issue 1 Pages 10-16

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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.

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