Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models Export

@article{Daunizeau09, 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.}, author = {Daunizeau, J. and Friston, K. J. and Kiebel, S. J.}, citeulike-article-id = {5441572}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.physd.2009.08.002}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0167278909002425}, day = {01}, doi = {10.1016/j.physd.2009.08.002}, issn = {01672789}, journal = {Physica D: Nonlinear Phenomena}, keywords = {dcm, variational\_calculus}, month = {November}, number = {21}, pages = {2089--2118}, posted-at = {2009-10-28 11:48:15}, priority = {2}, title = {Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models}, url = {http://dx.doi.org/10.1016/j.physd.2009.08.002}, volume = {238}, year = {2009} }

TY - JOUR ID - Daunizeau09 L3 - citeulike-article-id:5441572 N2 - 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. IS - 21 JF - Physica D: Nonlinear Phenomena SN - 01672789 EP - 2118 TI - Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models VL - 238 SP - 2089 KW - dcm KW - variational_calculus AU - Daunizeau, J AU - Friston, KJ AU - Kiebel, SJ PY - 2009/11/01/ UR - http://dx.doi.org/10.1016/j.physd.2009.08.002 ER -