On the Mathematical Consequences of Binning Spike Trains

On the Mathematical Consequences of Binning Spike Trains

We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochastic process that is no longer Markov but is instead a variable-length Markov chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs ...

Modelling spike trains and extracting response latency with Bayesian binning.

The peristimulus time histogram (PSTH) and the spike density function (SDF) are commonly used in the analysis of neurophysiological data. The PSTH is usually obtained by binning spike trains, the SDF being a (Gaussian) kernel smoothed version of the PSTH. While selection of the bin width or kernel size is often relatively arbitrary there have been recent attempts to remedy this situation (Shima...

The Statistics of Spike Trains

The timecourse of every action potential (AP) in a cell measured at the soma might not be identical, due to differences in the open channel configuration. However, axons tend to contain only the Na and K channels needed for AP propagation, and therefore exhibit little or no timecourse variation. Further, there is no experimental evidence I am aware of to indicate that AP shape affects vesicle r...

Neuronal Spike Trains

ABsTRAcr In a growing class of neurophysiological experiments, the train of impulses ("spikes") produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stocha...

Statistical models of spike trains∗