Trial-to-Trial Variability and its Effect on Time-Varying Dependence Between Two Neurons
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The joint peristimulus time histogram (JPSTH) and cross-correlogram provide a visual representation of correlated activity for a pair of neurons, and the way this activity may increase or decrease over time. In a companion paper (Cai et al. 2004a) we showed how a Bootstrap evaluation of the peaks in the smoothed diagonals of the JPSTH may be used to establish the likely validity of apparent time-varying correlation. As noted by Brody (1999a,b) and Ben-Shaul et al. (2001), trial-to-trial variation can confound correlation and synchrony effects. In this paper we elaborate on that observation, and present a method of estimating the time-dependent trial-to-trial variation in spike trains that may exceed the natural variation displayed by Poisson and non-Poisson point processes. The statistical problem is somewhat subtle because relatively few spikes per trial are available for estimating a firing-rate function that fluctuates over time. The method developed here uses principal components of the trial-to-trial variability in firing rate functions to obtain a small number of parameters (typically two or three) that characterize the deviation of each trial's firing rate function from the across-trial average firing rate, represented by the smoothed PSTH. The Bootstrap significance test of Cai et al. (2004a) is then modified to accommodate these general excitability effects. This methodology allows an investigator to assess whether excitability effects are constant or time-varying, and whether they are shared by two neurons. It is shown that trial-to-trial variation can, in the absence of synchrony, lead to an increase in correlation in spike counts between two neurons as the length of the interval over which spike counts are computed is increased. In data from two V1 neurons we find that highly statistically significant evidence of dependence disappears after adjustment for time-varying trial-to-trial variation.