zbMATH — the first resource for mathematics

Akaike causality in state space. Instantaneous causality between visual cortex in fMRI time series. (English) Zbl 1122.92044
Summary: We present a new approach of explaining instantaneous causality in multivariate fMRI time series by a state space model. A given single time series can be divided into two noise-driven processes, a common process shared among multivariate time series and a specific process refining the common process. By assuming that noises are independent, a causality map is drawn using Akaike’s noise contribution ratio theory. The method is illustrated by an application to fMRI data recorded under visual stimulation.
92C55 Biomedical imaging and signal processing
Full Text: DOI
[1] Akaike H (1968) On the use of a linear model for the identification of feedback systems. Ann Inst. Stat Math 20(3):425–439 · Zbl 0198.51202 · doi:10.1007/BF02911655
[2] Aoki M (1990) State space modeling of time series. Springer, New York · Zbl 0762.54029
[3] Åström KJ, Kallstrom CG (1973) Application of system identification techniques to the determination of ship dynamics. In: Eykhoff P (ed) Identification and system parameter estimation. North-Holland, Amsterdam
[4] Baccalá LA, Sameshima K (2001) Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84:463–474 · Zbl 1160.92306 · doi:10.1007/PL00007990
[5] Büchel C, Friston KJ (1997) Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. Cereb Cortex 7:768–778 · doi:10.1093/cercor/7.8.768
[6] Fukunishi K (1977) Diagnostic analyses of a nuclear power plant using multivariate autoregressive processes. Nucl Sci Eng 62(5):215–225
[7] Geweke JF (1982) Measurement of linear dependence and feedback between multiple time series. J Am Stat Assoc 77:304–324 · Zbl 0492.62078 · doi:10.2307/2287238
[8] Grewal MS, Andrews AP (2001) Kalman filtering: theory and practice using MATLAB, 2nd edn. Wiley, New York
[9] Harrison L, Penny WD, Friston K (2003) Multivariate autoregressive modeling of fMRI time series. NeuroImage 19:1477–1491 · doi:10.1016/S1053-8119(03)00160-5
[10] Harvey AC (1989) Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge
[11] Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82:35–45
[12] Kamiński MJ, Blinowska KJ (1991) A new method of the description of the information flow in the brain structures. Biol Cybern 65:203–210 · Zbl 0734.92003 · doi:10.1007/BF00198091
[13] Kitagawa G, Gersch W (1996) Smoothness priors analysis of time series. Springer, New York · Zbl 0853.62069
[14] Mehra RK (1971) Identification of stochastic linear dynamic systems. Am Inst Aeronaut Astronaut J 9:28–31 · Zbl 0249.93047
[15] Otomo T, Nakagawa T, Akaike H (1972) Statistical approach to computer control of cement rotary kilns. Automatica 8:35–48 · doi:10.1016/0005-1098(72)90008-8
[16] Saito Y, Harashima H (1981) Tracking of informations within multichannel EEG record, causal analysis in EEG. In: Yamaguchi N, Fujisawa K (eds) Recent advances in EEG and EMG data processing. Elsevier, Amsterdam, pp 133–146
[17] Sorenson HW (1985) Kalman filtering: theory and application. IEEE Press
[18] Valdés-Sosa P, Jimenez JC, Riera J, Biscay R, Ozaki T (1999) Nonlinear EEG analysis based on a neural mass model. Biol Cybern 81:348–358 · Zbl 0960.92016
[19] Wong KFK (2005) Multivariate time series analysis of heteroscedastic data with application to neuroscience. PhD thesis, Graduate University for Advanced Studies
[20] Yamashita O, Sadato N, Okada N, Ozaki T (2005) Evaluating frequency-wise directed connectivity of bold signals applying relative power contribution with the linear multivariate time series models. NeuroImage 25:478–490 · doi:10.1016/j.neuroimage.2004.11.042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.