[Eeglablist] Methodological question on connectivity

[Jeff Cromwell]

Hi Ryan and Marco, It has more to do with the underlying probability density function for the data at each frequency as well as nonstationarity. If you have normality and stationarity, you can have linearity in the first and second conditional moments which is the foundation for Granger's test and you are off and running--choosing the size of the window is a seminal problem in both the time and frequency domain--just use several and go with a measure of robustness.   The first question is the empirical PDF at each frequency and maybe you can transform the data to get normality and stationarity.  This has been the standard practice since 1970. Otherwise, linearity with third and perhaps fourth (kurtosis) conditional moment moments like the finance literature with GARCH or use a nonlinear functional form for the causality test.   This requires a theory of brain dynamics at different frequencies...Hmmm. Remember brain modeling at different frequencies is the same as stock price modeling at different intervals, i.e. hourly, daily, month, quarter, etc.  That research will provide more insight than the neuroscience literature which is just now using 20 year old techniques and it might help with your investments.  :-) The main question is what conditional moment is of interest here that will provide the most predictive power.  It could be the third-Skewness.
Thanks,
Jeff B. Cromwell, PhD www.thecromwellworkshop.com 
 Date: Thu, 3 May 2012 21:24:46 -0400
From: mcginn.ryan at gmail.com
To: marco.rotonda at gmail.com
CC: eeglablist at sccn.ucsd.edu
Subject: Re: [Eeglablist] Methodological question on connectivity

Hi Marco,
There is no reason why you would not be able to use Granger causality in this case.  Granger causality is not strictly an event-dependent measure.  Nevertheless, the brain state may not be transient even though the external manipulations (in this case hypnosis) may be.

The temporal window for granger causality (or the order of the analysis - a measure of what amount of signal is used in prediction) is a difficult thing to set, in general.  There are a number of information criteria (such as the aikake information criterion) that may help, but there is no definitive answer here, as far as I am aware.  What you are essentially asking is what is the memory of the system - i.e. what amount of time previous to a given event is necessary to predict it?

As to whether granger causality is correct, it is likely not correct; however, it may give some useful information.  The standard Granger causal measure is linear and as such does not strictly apply to highly nonlinear systems such as the brain.  It is also not defined in the frequency domain, as are some newer methods such as partial directed coherence.  Since the brain appears to rely on frequency, this may be a poor assumption.  Granger's original paper is a good one, and worth the read.

Ryan

On Wed, May 2, 2012 at 8:08 AM, Marco Rotonda <marco.rotonda at gmail.com> wrote:

Hi all,

I have some methodological questions on connectivity and I would like

to share you my doubts in the hope to solve them.



I would like to ask you if I could apply Granger Causality or other

connectivity analysis to a non transient event.

I mean I would like to know if it is possible to analyse an hypnosis induction.

In this case I have not many events to check but only one long session

where I could take 2-3 minutes in between.

I would like to analyze at the beginning, during the induction and

after the induction what's going on.



So now my questions are:

- is it correct to think using GC in this case?

- is it correct to take these 3 moments during the induction and treat

them as 3 different conditions?

- if yes, how long should be the ideal temporal window (in classical

FFT analysis is 4 seconds)





Thanks in advance



Marco

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