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

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  • SAITO Motoki
    Department of Electrical, Electronics and Computer Engineering, Waseda University
  • ENOMOTO Tsuyoshi
    Department of Electrical, Electronics and Computer Engineering, Waseda University, CREST, JST.
  • MATSUMOTO Takashi
    Department of Electrical, Electronics and Computer Engineering, Waseda University, CREST, JST.

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Other Title
  • 非線形ダイナミカルシステムの「モデル周辺ゆう度」重み付き再構成と予測
  • ヒセンケイ ダイナミカル システム ノ モデル シュウヘンユウ ド オモミツキ サイコウセイ ト ヨソク カイソウ ベイズテキ アプローチ
  • A Hierarchical Bayesian Approach
  • 階層ベイズ的アプローチ

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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 : <BR>(i) Formulae for posterior distributions of parameters, hyper parameters as well as models via Bayes formula.<BR>(ii) Derivation of predictive distributions of future values taking into account model marginal likelihoods.<BR>(iii) Using several drastic approximations for computing predictive mean of time series incorporating model marginal likelihoods.<BR>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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