Statistical limits for detecting change in the cumulative sum derivative of the peristimulus time histogram

doi:10.1016/0165-0270(86)90068-3

Journal of Neuroscience Methods

Volume 17, Issues 2–3, August 1986, Pages 153-166

https://doi.org/10.1016/0165-0270(86)90068-3 Get rights and content

Abstract

The peristimulus time histogram (psth) provides a means of correlating the discharges of neurones with other events. The cumulative sum (cusum) derived from the psth facilitates the detection of small changes in the psth that may be obscured by random fluctuations in counts. The cusum integrates differences from the mean control level of counts in the psth. Any signal in the data that is related to the stimulus appears as a slope in the cusum. Psth's constructed from the rhythmic discharges of single neurones are shown to contain periodical fluctuations in counts that arise from refractoriness. This periodicity results in a cusum which deviates less from the horizontal line than predicted from a Poisson distribution of points. The more regular the spike train, i.e., the lower the coefficient of variation of the distribution of interspike intervals, the flatter is the cusum. The theory of stochastic point processes is used to derive an algorithm for calculating the best approximation of variance of the cusum. Significance limits set at 3 standard deviations of the cusum are shown to provide a good fit to cusums for unit discharges over a wide range of coefficients of variation (0.09–0.60).

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Trial time warping to discriminate stimulus-related from movement-related neural activity
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Therefore, a critical problem in the cortical physiology of behaving animals is to determine whether the response of neurons is related to the different aspects of a task. Different algorithms have been implemented to determine the onset latency of neurons using parametric (Ellaway, 1978; Seal et al., 1983; Davey et al., 1986; Baker and Gerstein, 2001) or nonparametric methods (Sanderson, 1980; Nawrot et al., 2003; Ventura, 2004). Most of these methods take into account the trial-to-trial variability of neuronal activity and can determine with different levels of accuracy the onset response latency, especially to sensory stimuli.
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Commencing at the first bin (−50 ms), and stepping through the CUSUM bin by bin, the presence of significant deflections from the previous bin were evaluated (p < 0.0025). These significant deflections define a peak in the cross-correlogram (Davey et al., 1986). All adjacent bins remaining above a 90% confidence interval were also defined as significant, defining the peak width in the cross-correlogram.
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Research paperStatistical limits for detecting change in the cumulative sum derivative of the peristimulus time histogram

Abstract

J. Electroencephalogr. Clin. Neurophysiol.

J. Neurosci. Meth.

Biophys. J.

Biophys. J.

The statistical analysis of series of events

The Theory of Stochastic Processes

The variability in discharge of fusimotor neurones in the decerebrated cat

Exp. Brain Res.

An application of cumulative sum technique (cusums) to neurophysiology

J. Physiol. (London)

The cumulative sum derivative of the PSTH in the analysis of correlated events in the nervous system

Research paper
Statistical limits for detecting change in the cumulative sum derivative of the peristimulus time histogram