Abstract
In this interdisciplinary contribution we discuss a number of problems related to stochastic models and statistical methods used in electroencephalography. The main part of the paper is devoted to the assumption of a Gaussian process. We present a variety of methods to check empirically such an assumption, together with examples. The deviations from a Gaussian process which occur in EEG analysis are interpreted in terms of non-linear dynamics; the input-output-map is assumed to be well represented by a Volterra series.
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References
Akaike, H. (1970). Statistical predictor identification. Ann. Inst. Statist. Math. 22, 203–17
Bingham, C., M.D. Godfrey, J.W. Tukey (1967). Modern techniques of power spectrum estimation. IEEE Trans. Audio Electroac. AU-15, 56–66
Brillinger, D.R. (1970). The identification of polynomial systems by means of higher order spectra. J. Sound Vib. 12, 301–313
Brillinger, D.R. (1975). Time series analysis. Holden-Day, San Francisco.
Brillinger, D.R., M. Rosenblatt (1967). Asymptotic theory of estimates of k-th order spectra. Spectral Analysis of Time Series, 153–186, ed. B. Harris, J. Wiley, New York
Cooley, J.S., J.W. Tukey (1965). An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 267–301
Dumermuth, G., P.J. Huber, B. Kleiner, T. Gasser (1971). Analysis of the interrelations between frequency bands of the EEG by means of the bispectrum. Electroenceph. Clin. Neurophysiol. 31, 137–148
Dumermuth, G., Th. Gasser, B. Lange (1975). Aspects of EEG analysis in the frequency domain, CEAN, ed. G. Dolce & H. Künkel, 429–457, G.Fischer Stuttgart
Gasser, Th. (1977). General characteristics of the EEG as a signal. EEG-Informatics, ed. A. Rémond, 37–52, Elsevier/North Holland, Amsterdam.
Gevins, A.S., Ch.L. Yeager, S.L. Diamond, J.P. Spire, G.M. Zeitlin, A.H. Gevins (1975). Automated analysis of the electrical activity of the human brain. Proc. IEEE, 63, 1382–1399
Lopes da Silva, F.H., A. Dijk, H. Smits (1975). Detection of non-stationarities in EEG using the autoregressive model. CEAN, ed. G. Dolce & H. Künkel, 180–199, G. Fischer, Stuttgart
Marti, J.T. (1971). On the approximation of continuous non-linear operators in normed spaces by polynomial operators, ZAMP 22, 991–996
Rozanov, Y. (1967). Stationary stochastic processes. Holden-Day, San Francisco.
Wiener, N. (1958). Non-linear problems in random theory. Cambridge, MIT-Press
Zetterberg, L.H. (1969). Estimation of parameters for a linear difference equation with application to EEG-analysis. Math. Biosci. 5, 227–275
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© 1979 Springer-Verlag
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Gasser, T., Dumermuth, G. (1979). Non-gaussianity and non-linearity in electroencephalographic time series. In: Kohlmann, M., Vogel, W. (eds) Stochastic Control Theory and Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009397
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DOI: https://doi.org/10.1007/BFb0009397
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09480-7
Online ISBN: 978-3-540-35211-2
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