Information transfer in continuous processes

Physica D: Nonlinear Phenomena

Volumn 166, Issue 1-2, 2002, Pages 43-62

  Kaiser, A ^a   Schreiber, T ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

Information theory; Information transfer; Mutual information; Non parametric estimation; Stochastic dependence

Indexed keywords

EID: 0036610922     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00432-3     Document Type: Article

References (34)

1. M.G. Rosenblum A.S. Pikovsky Detecting direction of coupling in interacting oscillators Phys. Rev. E 64 2001 045202(R)
2. J. Arnhold P. Grassberger K. Lehnertz C.E. Elger A robust method for detecting interdependences: application to intracranially recorded EEG Physica D 134 1999 419
3. M.G. Rosenblum A.S. Pikovsky J. Kurths Phase synchronisation of chaotic attractors Phys. Rev. Lett. 76 1996 1804
4. M. Le Van Quyen C. Adam M. Baulac J. Martinerie F.J. Varela Non-linear interdependences of EEG signals during intracranial ictal activities Brain Res. 792 1998 24
5. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization, Cambridge University Press, Cambridge, 2001.
6. T. Schreiber Measuring information transfer Phys. Rev. Lett. 85 2000 461
7. P. Billingsley, Ergodic theory and information, Wiley, New York, 1965.
8. C.E. Shannon, W. Weaver, The Mathematical Theory of Information, University of Illinois Press, Urbana, IL, 1949.
9. G. Jumarie, Relative Information: Theories and Applications, Springer Series in Synergetics, Vol. 47, Springer, Berlin, 1990.
10. T.M. Cover, J.A. Thomas, Elements of Information Theory, Wiley Series in Telecommunications, Wiley, New York, 1991.
11. S. Kullback, Information Theory and Statistics, Wiley, New York, 1959.
12. D. Prichard J. Theiler Generalized redundancies for time series analysis Physica D 84 1995 476
13. A.M. Fraser H.L. Swinney Independent coordinates for strange attractors from mutual information Phys. Rev. A 33 1986 1134
14. G.A. Darbellay An estimator of the mutual information based on a criterion for independence Comput. Stat. Data Anal. 32 1999 1
15. M. Palus Detecting nonlinearity in multivariate time series Phys. Lett. A 213 1996 138
16. B. Pompe Measuring statistical dependences in a time series J. Stat. Phys. 73 1993 587
17. R. Hegger H. Kantz L. Matassini T. Schreiber Coping with non-stationarity by over-embedding Phys. Rev. Lett. 84 2000 4092
18. H. Bauer, Wahrscheinlichkeitstheorie, 4th Edition, Walter de Gruyter, Berlin, 1991.
19. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, MA, 1997.
20. A.N. Kolmogorov, Information theory and the theory of algorithms, Selected Works, Vol. 3, Kluwer, Dordrecht, 1993.
21. K. Kaneko Lyapunov analysis and information flow in coupled map lattices Physica D 23 1986 436
22. J.A. Vastano H.L. Swinney Information transport in spatiotemporal systems Phys. Rev. Lett. 60 1988 1773
23. H. Bauer, Maß- und Integrationstheorie, 2nd Edition, Walter de Gruyter, Berlin, 1992.
24. P. Billingsley, Probability and Measure, Wiley Series in Probability and Mathematical Statistics, 3rd Edition, Wiley, New York, 1995.
25. P. Grassberger Finite sample corrections to entropy and dimension estimates Phys. Lett. A 128 1988 369
26. P. Grassberger Generalizations of the Hausdorff dimension of fractal measures Phys. Lett. A 107 1985 101
27. H. Herzel A.O. Schmitt W. Ebeling Finite sample effects in sequence analysis Chaos Solitons Fract. 4 1994 97
28. M.S. Roulston Estimating the errors on measured entropy and mutual information Physica D 125 1999 285
29. M.S. Roulston Significance testing of information theoretic functionals Physica D 110 1997 62
30. T. Schreiber Spatio-temporal structure in coupled map lattices: two-point correlations versus mutual information J. Phys. A 23 1990 L393
31. T. Schreiber A. Schmitz Surrogate time series Physica D 142 2000 346
32. B.W. Silverman, Density estimation for statistics and data analysis, Monographs on Statistics and Applied Probability, Vol. 26, Chapman & Hall, London, 1986.
33. J. Theiler Spurious dimension from correlation algorithms applied to limited time series data Phys. Rev. A 34 1986 2427
34. D.R. Rigney, A.L. Goldberger, W. Ocasio, Y. Ichimaru, G.B. Moody, R. Mark, Multi-channel physiological data: description and analysis, in: A.S. Weigend, N.A. Gershenfeld (Eds.), Time Series Prediction: Forecasting the Future and Understanding the Past, Santa Fe Institute Studies in the Science of Complexity, Proc. Vol. XV, Addison-Wesley, Reading, MA, 1993.