Confidence Limits for Perievent Histograms

If the duration of experimental session is T (seconds) and we have N spikes in the session, then the neuron firing rate F (spikes per second) is:

F = N/T

Several options how to calculate neuron firing rate F are available. See Options below.

If the spike train is a Poisson train, the probability of the neuron to fire in the small bin of the size b (seconds) is

P = F*b

The expected bin count for the perievent histogram is then:

C = P*NRef, where NRef is the number of the reference events.

The value C is used for drawing the Mean Frequency in the Perievent Histograms and Cross- and Autocorrelograms.

The confidence limits for bin counts are calculated using the assumption that the bin count has a Poisson distribution with mean C.

Assume that a random variable S has a Poisson distribution with parameter (and mean) C. Then, the 99% confidence limits are calculated as follows:

Low Conf. = x such that Prob(S < x) = 0.005

High Conf. = y such that Prob(S > y) = 0.005

If C < 30, NeuroExplorer uses the actual Poisson distribution

Prob(S = K) = exp(-C) \* (C^K) / K!, where C^K is C to the power of K,

to calculate the confidence limits.

If C>= 30., the Gaussian approximation of the Poisson distribution is used. The approximation of Poisson distribution with mean C is a Gaussian distribution with both the mean and variance equal to C.

For example, for 99% confidence limits:

Low Conf. = C - 2.58*sqrt(C)

High Conf.= C + 2.58*sqrt(C)

Options

The following options to calculate the neuron firing rate F are available:

  • Use target and reference timestamps from selected time range and interval filter. T is the length of all the time intervals used in analysis, N is the number of spikes within these intervals.

  • Use all target and reference timestamps from the file. Here T is the total length of experimental session, N is the total number of spikes for a given neuron.

  • Use target timestamps from the time intervals corresponding to bins before zero. This option only works for a stimulation-type data. For example, if you stimulate every second and calculate Perievent Histogram with XMin=-0.2, XMax=0.2, NeuroExplorer can easily distinguish the spikes before and after the stimulus. However, if you stimulate every 200 ms, the spikes before the second stimulus are also the spikes after the first stimulus, so you cannot distinguish the spikes that should be used to calculate the mean firing rate. The algorithm:

    • For each reference event timestamp r, a time interval (r+XMin, r) is created (where XMin is Perievent Histogram or Crosscorrelogram time axis minimum parameter; XMin should be negative).

    • T is calculated as the length of all (r+XMin, r) intervals that do not overlap.

    • N is calculated as the number of spikes in these intervals.

    • If more than 5% of intervals overlap, F is set to zero.

  • Use target timestamps from interval filter. Use this option when you want to calculate the neuron firing rate using spikes from an interval filter that is different from the interval filter specified in the Data Selection page. T is the length of all the time intervals of the specified interval filter, N is the number of spikes within these intervals.

Reference

Abeles M. Quantification, smoothing, and confidence limits for single-units histograms. Journal of Neuroscience Methods. 5(4):317-25, 1982