TFMVAR Time-Frequency MVAR analysis time-frequency analysis of multivariate stochastic processes. [R] = tfmvar(s,TRIG,T,MOP,f,Fs, [CL,group]) INPUT: s signal data (one channel per column) TRIG trigger time points (in SAMPLES) T windows definition; each column defines one window) T(1,:) and T(2,:) indicate start and end [in samples], respectivly MOP model order of the MVAR model f designated frequencies Fs sampling rate. [CL,group] is OPTIONAL CL are the labels for different classes, conditions, states. CL must be a column vector having the same length than TRIG group is useful for controlling the resampling same numbers indicate that member belongs to the same group. E.g. if data from several subjects are concatanated, and the the trials of each subject have the same numbers, the standard error of the group-statistic is estimated. If group is empty [default], each trial gets a different number; Accordingly, a trial-based leave-on-out-method (LOOM) is used, for computing the standard error. OUTPUT: M and SE contain the mean and the standard error of the mean of the following characteristic parameters. The size of the parameters is defined by the number of channels, the number of windows the number of designated frequencies [size(s,2), size(T,1), length(f)] respectively. univariate: S1 Autospectra logS1 log(abs(S1)) AR1 univariate autoregressive parameters C1 variance of predication error multivariate: S Auto- and Cross-spectra h transfer function logS log(abs(S)) logh log(abs(h)) y1i imaginary part of amplitude spectra h1i imaginary part of transfer function phaseS phase of S phaseh phase of h COH coherence coh coherence neglecting the cross-correlation due to the innovation process pCOH partial coherence PDC partial directed coherence [2, 5] DTF directed transfer function [3, 6] dDTF modified DTF [8] ffDTF modified DTF [8] AR MVAR parameters C covariance matrix of the innovation process DC directed granger causality [2,3,5,6] GGC Geweke's Granger Causality (not quite the same as in [12,13] Af Frequency transform of A(z) [R] = tfmvar(s,TRIG,T,MOP,f,Fs) R is a struct containing M and SE as well as a few more parameters for visualization The standard error is calculated with a jackknife-method, based on LEAVE-K-TRIALs-OUT. Therefore, the SE need to be rescaled, depending on the needs [10,11]. SE standard error of the mean from the bootstrap results This has usually no common meaning (pretty much useless). SE*(N-K)^(1/2) standard deviation of the means from the bootstrapping It can be interpreted as the standard error of the total mean (across all trials). This value becames smaller if the number of trials increase. SE*(N-K) average standard error of the mean (based on a single trial). This value provides a realistic value for the confidence interval of the estimates and can be used to test the significance. SE*(N-K)*N^(1/2) [estimated] standard deviation of a single trial estimate This value is important for a single-trial classification. see also: tsa/MVAR, tsa/MVFREQZ, PLOTA Reference(s): [1] Kay S. M., Marple S. L., Spectrum Analysis - A Modern Perspective, Proc. IEEE, 1981 [2] Baccala L. A., Sameshima K., Partial Directed Coherence: A New Concept in Neural Structure Determination, Biological Cybernetics 84, 2001 [3] Kaminski M., Blinowska K., Szelenberger W., Topographic Analysis of Coherence and Propagation of EEG Activity During Sleep and Wakefulness, Electroencephalography and Clinical Neurophysiology 102, 1997 [4] Franaszczuk P. J., Bergey G. K., An Autoregressive Method for the Measurement of Synchronization of Interictal and Ictal EEG Signals, Biological Cybernetics 81, 1999 [5] Sameshima K., Baccala L. A., Using Partial Directed Coherence to Describe Neuronal Ensemble Interactions, Journal of Neuroscience Methods 94, 1999 [6] Kaminski M., Ding M., Truccolo W. A., Bressler S. L., Evaluating Causal Relations in Neural Systems: Granger Causality, Directed Transfer Function and Statistical Assessment of Significance, Biological Cybernetics 85, 2001 [7] Liang H., Ding M., Bressler S. L., On the Tracking of Dynamic Functional Relations in Monkey Cerebral Cortex, Neurocomputing, 2000 [8] Korzeniewska A., Manczak M., Kaminski M., Blinowska K. J., Kasicki S., Determination of Information Flow Direction Among Brain Structures By a Modified Directed Transfer Function (dDTF) Method, Journal of Neuroscience Methods 125, 2003 [9] A. Schl\"ogl, Comparison of Multivariate Autoregressive Estimators. Signal processing, Elsevier B.V. (in press). available at http://dx.doi.org/doi:10.1016/j.sigpro.2005.11.007 [10] http://www.physics.utah.edu/~detar/phycs6730/handouts/jackknife/jackknife/jackknife.html [11] http://www-stat.stanford.edu/~susan/courses/s208/node16.html [12] Geweke J., 1982. J.Am.Stat.Assoc., 77, 304-313. [13] Bressler S.L., Richter C.G., Chen Y., Ding M. (2007) Cortical fuctional network organization from autoregressive modelling of loal field potential oscillations. Statistics in Medicine, doi: 10.1002/sim.2935

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