1. Friston K.J., Harrison L., Penny W. Dynamic causal modelling. Neuroimage. 2003;19:1273–1302. [PubMed] 2. Kiebel S.J., Garrido M.I., Friston K.J. Dynamic causal modelling of evoked responses: The role of intrinsic connections. Neuroimage. 2007;36:332–345. [PubMed] 3. Judd K., Smith L.A. Indistinguishable states II: The imperfect model scenario. Physica D. 2004;196:224–242.

4. Saarinen A., LInne M.L., Yli-Harja O. Stochastic differential equation model for cerebellar granule cell excitability. Plos Comput. Bio. 2008;4 [PMC free article] [PubMed] 5. Herrmann C.S. Human EEG responses to 1–100 Hz flicker: Resonance phenomena in visual cortex and their potential correlation to cognitive phenomena. Exp. Brain Res. 1988;137:149–160. [PubMed] 6. Jimenez J.C., Ozaki T. An approximate innovation method for the estimation of diffusion processes from discrete data. J. Time Ser. Anal. 2006;76:77–97.

7. Friston K.J., Trujillo N.J., Daunizeau J. DEM: A variational treatment of dynamical systems. Neuroimage. 2008;41:849–885. [PubMed] 8. A. Joly-Dave, The fronts and Atlantic storm-track experiment (FASTEX): Scientific objectives and experimental design, Bull. Am. Soc. Meteorol, Mto-France, Toulous, France, 1997. http://citeseer.ist.psu.edu/496255.html. 9. Wikle C.K., Berliner L.M. A Bayesian tutorial for data assimilation. Physica D. 2007;230:1–16.

10. Briers M., Doucet A., Maskell S. Smoothing algorithm for state-space models. IEEE Trans. Signal Process. 2004

11. Kushner H.J. Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. vol. 129. Accademic Press; New York: 1977. (Mathematics in Science and Engineering).

12. Pardoux E. vol. 1464. Springer-Verlag; 1991. Filtrage non-lineaire et equations aux derivees partielles stochastiques associees, Ecole d’ete de probabilites de Saint-Flour XIX - 1989. (Lectures Notes in Mathematics).

13. F.E. Daum, J. Huang, The curse of dimensionality for particle filters, in: Proc. of IEEE Conf. on Aerospace, Big Sky, MT, 2003.

14. Julier S., Uhlmann J., Durrant-Whyte H.F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Automat. Control. 2000

16. Budhiraja A., Chen L., Lee C. A survey of numerical methods for nonlinear filtering problems. Physica D. 2007;230:27–36.

17. Arulampalam M.S., Maskell M., Gordon N., Clapp T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 2002;50(2) (special issue)

18. Doucet A., Tadic V. Parameter estimation in general state-space models using particle methods. Ann. Inst. Stat. Math. 2003;55:409–422.

19. Wan E., Nelson A. Dual extended Kalman filter methods. In: Haykin S., editor. Filtering and Neural Networks. Wiley; New York: 2001. pp. 123–173. (Chapter 5)

20. Yedidia J.S. MIT Press; 2000. An Idiosyncratic Journey Beyond Mean Field Theory.

21. M. Beal, Variational algorithms for approximate Bayesian inference, University of London Ph.D. Thesis, 2003.

23. Wang B., Titterington D.M. Convergence and asymptotic normality of variational Bayesian approximations for exponential family models with missing values. ACM Internat. Conf. Proc. Series. 2004;70:577–584.

24. Roweis S.T., Ghahramani Z. An EM algorithm for identification of nonlinear dynamical systems. In: Haykin S., editor. Kalman Filtering and Neural Networks. 2001. http://citeseer.ist.psu.edu/306925.html 25. Valpola H., Karhunen J. An unsupervised learning method for nonlinear dynamic state-space models. Neural Comput. 2002;14(1):2547–2692.

26. C. Archambeau, D. Cornford, M. Opper, J. Shawe-Taylor, Gaussian process approximations of stochastic differential equations, in: JMLR: Workshop and Conferences Proceedings, vol. 1, 2007, pp. 1–16.

27. Wang B., Titterington D.M. Lack of consistency of mean-field and variational Bayes approximations for state-space models. Neural Process. Lett. 2004;20:151–170.

28. Friston K.J., Mattout J., Trujillo-Barreto N., Ashburner J., Penny W. Variational free-energy and the Laplace approximation. Neuroimage. 2007;34:220–234. [PubMed] 29. Gray R.M. Springer-Verlag; 1990. Entropy and Information Theory.

30. Tanaka T. A theory of mean field approximation. In: Kearns M.S., Solla S.A., Cohn D.A., editors. Advances in Neural Information Processing Systems. 2001. http://Citeseer.ist.psu.edu/303901.html 31. Tanaka T. Information geometry of mean field approximation. Neural Comput. 2000;12:1951–1968. [PubMed] 32. G.E. Hinton, D. Van Camp, Keeping neural networks simple by minimizing the description length of the weights, in: Proc. of COLT-93, 1993, pp. 5–13.

33. Carlin B.P., Louis T.A. Text in Statistical Science. 2nd ed. Chapman and Hall/CRC; 2000. Bayes and empirical Bayes methods for data analysis.

34. C. Robert, L’analyse statistique Bayesienne, Ed. Economica, 1992.

35. Kloeden P.E., Platen E. third ed. Springer; 1999. Numerical Solution of Stochastic Differential Equations, Stochastic Modeling and Applied Probability.

36. Ozaki T. A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: A local linearization approach. Statistica Sinica. 1992;2:113–135.

37. Kleibergen F., Van Dijk H.K. Non-stationarity in GARCH models: A Bayesian analysis. J. Appl. Econom. 1993;8:S41–S61.

38. Meyer R., Fournier D.A., Berg A. Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter. Econom. J. 2003;6:408–420.

39. Sornette D., Pisarenko V.F. Properties of a simple bilinear stochastic model: Estimation and predictability. Physica D. 2008;237:429–445.

40. Tropper M.M. Ergodic and quasideterministic properties of finite-dimensional stochastic systems. J. Stat. Phys. 1977;17:491–509.

41. Björck A. SIAM; Philadelphia: 1996. Numerical Methods for Least Squares Problems.

42. Lacour C. Nonparametric estimation of the stationary density and the transition density of a Markov chain. Stoch. Process. Appl. 2008;118:232–260.

43. Angeli D., Ferrell J.E., Sontag E.D. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc. Nat. Atl. Sci. 2004;101:1822–1827. [PubMed] 44. Lorenz E.N. Deterministic nonperiodic flow. J. Atmospheric Sci. 1963;20:130–141.

46. Fitzhugh R. Impulses and physiological states in theoretical models of nerve membranes. Biophys. J. 1961;1:445–466. [PubMed] 47. J.S. Nagumo, S. Arimoto, S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 1962 50, pp. 2061–2070.

48. Gill R.D., Levit B.Y. Applications of the van trees inequality: a Bayesian Cramer–Rao bound. Bernouilli. 1995;1:59–79.

49. Slotine J., Li W. Prentice-Hall, Inc; New Jersey: 1991. Applied Nonlinear Control.

50. Gardner W.A., Napolitano A., Paura L. Cyclostationarity: Half a century of research. Sig. Process. 2006;86:639–697.

51. Gelman A., Carlin J.B., Stern H.S., Rubin D.B. 2d ed. Chapman & Hall/CRC editions; 2004. Bayesian Data Analysis.

52. Hanson F.B., Ryan D. Mean and quasideterministic equivalence for linear stochastic dynamics. Math. Biosci. 1988;93:1–14. [PubMed] 53. Friston K.J., Ashburner J., Kiebel S.J., Nichols T., Penny W.D. Academic Press, Elsevier Ltd.; 2006. Statistical Parametric Mapping, The Analysis of Functional Brain Images. ISBN: 10: 0-12-372560-7.

54. Petrelis F., Aumaitre S., Mallick K. Escape from a potential well, stochastic resonance and zero-frequency component of the noise. Europhys. Lett. 2007;79:40004.

55. Ghahramani Z., Hinton G.A. Variational learning for switching state-space models. Neural Comput. 2000;12:831–864. [PubMed] 56. Ito H.M. Ergodicity of randomly perturbed Lorenz model. J. Stat. Phys. 1984;35:151–158.

57. Turbiner A. Anharmonic oscillator and double-well potential: Approximating eigenfunctions. Lett. Math. Phys. 2005;74:169–180.

58. Crisan D., Lyons T. A particle approximation of the solution of the Kushner–Stratonovitch equation. Probab. Theory Related Fields. 1999;115:549–578.