Trial-to-Trial Variability and its Effect on
Time-Varying Dependence Between Two Neurons
Can Cai, Robert E. Kass, and Valérie Ventura
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.
we showed how a Bootstrap evaluation of the peaks in
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.
can confound correlation and synchrony effects. In this paper we
elaborate on that observation, and present a method of estimating
trial-to-trial variation in spike trains that may exceed the natural
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.
Keywords: Bootstrap, Correlation, Cross-correlogram,
Excitability Effects, Firing Rate, Latency Effects, Non-Poisson
Spiking, Peri-Stimulus Time Histogram, Point Process, Principal
Components, Smoothing, Spike Train Analysis, Trial-to-Trial Variability