¥ Check the effectiveness of GLSQ
pre-whitening solution by examining pre-whitened residuals
H Pre-whitening: applying a linear
transformation to the time series data to de-correlate the noise
oSymbolically, R-1/2 where R is the correlation matrix
¥ After pre-whitening, residuals (difference between data and fitted time series) should be (mostly)
uncorrelated
¥ Power spectrum of white noise is
flat
H Power spectrum = expected value of
absolute value of Fourier transform, averaged over an infinity of repeated identical
experiments
¥ Visually inspect graph of abs[FFT(pre-whitened residuals)]
H Should be flattish, with random
excursions
oThis is noise, after all, and we
donÕt have an infinity of data over which to average
¥ Next 4 slides:
H Graphs of ÒspectrumÓ for OLSQ and GLSQ
using ARMA(1,1), AR(1), and MA(1) correlation models (generated
using interactive AFNI, of course)
H For 3 strongly ÒactiveÓ voxels in one
subject (block design: 30 s blocks; NIH
3T)
H Then the single subject activation maps
for 6 types of analysis