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  Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models

Daunizeau, J., Friston, K. J., & Kiebel, S. J. (2009). Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models. Physica D: Nonlinear Phenomena, 238(21), 2089-2118. doi:10.1016/j.physd.2009.08.002.

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 Creators:
Daunizeau, Jean, Author
Friston, Karl J., Author
Kiebel, Stefan J.1, Author              
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1External Organizations, ou_persistent22              

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Free keywords: Approximate inference; Model comparison; Variational Bayes; EM; Laplace approximation; Free-energy; SDE; Nonlinear stochastic dynamical systems; Nonlinear state-space models; DCM; Kalman filter; Rauch smoother
 Abstract: In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

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 Dates: 2009
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 512056
Other: P10677
DOI: 10.1016/j.physd.2009.08.002
 Degree: -

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Title: Physica D: Nonlinear Phenomena
  Other : Physica D
Source Genre: Journal
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Publ. Info: Amsterdam : North-Holland
Pages: - Volume / Issue: 238 (21) Sequence Number: - Start / End Page: 2089 - 2118 Identifier: ISSN: 0167-2789
CoNE: https://pure.mpg.de/cone/journals/resource/954925482641