m8ta
You are not authenticated, login. 

{763}  
I recently wrote a matlab script to measure & plot the autocorrelation of a spike train; to test it, I generated a series of timestamps from a homogeneous Poisson process: function [x, isi]= homopoisson(length, rate) % function [x, isi]= homopoisson(length, rate) % generate an instance of a poisson point process, unbinned. % length in seconds, rate in spikes/sec. % x is the timestamps, isi is the intervals between them. num = length * rate * 3; isi = (1/rate).*log(1rand(num, 1)); x = cumsum(isi); %%find the x that is greater than length. index = find(x > length); x = x(1:index(1,1)1, 1); isi = isi(1:index(1,1)1, 1); The autocorrelation of a Poisson process is, as it should be, flat: Above:
The problem with my recordings is that there is generally high longrange correlation, correlation which is destroyed by shuffling. Above is a plot of 1/isi for a noise channel with very high mean 'firing rate' (> 100Hz) in blue. Behind it, in red, is 1/shuffled isi. Noise and changes in the experimental setup (bad!) make the channel very nonstationary. Above is the autocorrelation plotted in the same way as figure 1. Normally, the firing rate is binned at 100Hz and highpass filtered at 0.005hz so that longrange correlation is removed, but I turned this off for the plot. Note that the suffled data has a number of different offsets, primarily due to differing longrange correlations / nonstationarities. Same plot as figure 3, with highpass filtering turned on. Shuffled data still has far more local correlation  why? The answer seems to be in the relation between individual isis. Shuffling isi order obviuosly does not destroy the distribution of isi, but it does destroy the ordering or pairwise correlation between isi(n) and isi(n+1). To check this, I plotted these two distributions:  Original log(isi(n)) vs. log(isi(n+1)  Shuffled log(isi_shuf(n)) vs. log(isi_shuf(n+1)  Closeup of log(isi(n)) vs. log(isi(n+1) using alphablending for a channel that seems heavily corrupted with electrocauterizer noise.  
{826}  
Studies in astronomical time series analysis. II  Statistical aspects of spectral analysis of unevenly spaced data Scargle, J. D.
