Trial-to-Trial Variability and Its Effect on Time-Varying Dependency Between Two Neurons

Abstract

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 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 in earlier studies by Brody and Ben-Shaul et al., 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 decomposes the spike-train variability into a stimulus-related component and a trial-specific component, allowing many degrees of freedom to characterize the former while assuming a small number suffices to characterize the latter. The Bootstrap significance test of the companion paper 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. In data from two V1 neurons we find that highly statistically significant evidence of dependency disappears after adjustment for time-varying trial-to-trial variation.

Conditional modeling and the jitter method of spike resampling

“…The basic, and quite plausible, counterexamples are forms of trial-to-trial variability, such as latency variations (Ventura 2004) or slowly varying common input, such as that due to internal variables not controlled by the experiment (Baker and Gerstein 2001;Czanner et al 2008;Grün et al 2003;Kass and Ventura 2006). One proposal for dealing with such concerns is to incorporate trial-varying firing rates into parametric models of the spiking process, which can again be tested, for example, by estimated trial-varying firing rates incorporated into bootstrap tests (Bair et al 2001;Ben-Shaul et al 2001;Brody 1999;Pauluis and Baker 2000;Ventura et al 2005b). Of course, in any such model the number of parameters that must be estimated from the data is proportional to the number of trials, and for this reason, at least, standard statistical issues concerning model complexity become very delicate.…”

“…In such a circumstance, even slow variations in firing rate will induce a peak in the crosscorrelation histogram at zero, and the peak will appear to be significant when measured, for example, against a corresponding cross-correlation histogram value produced by a "shuffle" (permutation) of trials of one or the other of the neurons. These effects have been widely discussed (Baker and Gerstein 2001;Brody 1998;Ventura et al 2005b). A peak at and around zero in a shuffle-corrected cross-correlation histogram is not, in and of itself, an artifact; common variation in firing rates across two neurons induces a statistical correlation in spike timings.…”

Spike Count Reliability and the Poisson Hypothesis

“…Hidden variables effectively act randomly, and thus, accounting for them involves making the rate function ( t) itself random (Ventura et al, 2005). A Poisson process equipped with a random rate function is a Cox process (Cox, 1955).…”

Analysis of Between-Trial and Within-Trial Neural Spiking Dynamics

“…The between-trial dynamics may represent random variations in the neuron's response to the same stimulus or changes in how the neuron responds to the stimulus. The former may represent noise (Brody 1999;Dayan and Abbott 2001;Lim et al 2006;Narayan et al 2006;Ventura et al 2005), whereas the latter may represent the evolution of a neuron's receptive field properties (Brown et al 2001;Gandolfo et al 2000;Kaas et al 1983;Mehta et al 1997;Merzenich et al 1984) or behavior-related changes such as learning and memory formation (Jog et al 1999;Wirth et al 2003;Wise and Murray 1999). The within-trial dynamics may reflect stimulusspecific or task-specific features of the neuron's responses (Lim et al 2006;Narayan et al 2006;Wirth et al 2003), short timescale biophysical properties, such as absolute and relative refractory periods and bursting, or longer timescale biophysical properties such as oscillatory modulations and other network and local regional characteristics (Dayan and Abbott 2001).…”

“…To go beyond use of raster plots, several authors have proposed analyses based on parametric or semiparametric statistical models to analyze between-and within-trial dynamics in neural activity (Brody 1999;Ventura et al 2005). In these analyses, the components of the between-and within-trial dynamics are estimated sequentially rather than simultaneously, and the effects of history dependence within trial are not considered.…”