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TFMVAR Time-Frequency MVAR analysis


function [R] = tfmvar(s,TRIG,T,MOP,f,Fs,cl)


 TFMVAR Time-Frequency MVAR analysis
   time-frequency analysis of 
   multivariate stochastic processes. 

 [R] = tfmvar(s,TRIG,T,MOP,f,Fs, [CL,group])

  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. 

         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. 

   S1        Autospectra
   logS1       log(abs(S1))
   AR1         univariate autoregressive parameters 
   C1          variance of predication error 

   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]. 
    standard error of the mean from the bootstrap results 
    This has usually no common meaning (pretty much useless). 
    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.     
    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 
    [estimated] standard deviation of a single trial estimate
    This value is important for a single-trial classification.  

 see also: tsa/MVAR, tsa/MVFREQZ, PLOTA

 [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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