Multichannel Systems NeuroExplorer - Manual (Page 51)

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2.6. Confidence Limits for Perievent Histograms
If the total time interval (experimental session) is T (seconds) and we have N spikes in the interval,
then the neuron frequency is:
F = N/T
Several options how to calculate neuron frequency F are available. See Options below.
Then 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 C are calculated using the assumption that C has a Poisson distribution.
Assume that a random variable S has a Poisson distribution with parameter 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 is used. For example, for 99% confidence limits:
Low Conf. = C - 2.58*sqrt(C);
High Conf.= C + 2.58*sqrt(C);
Reference
Abeles M. Quantification, smoothing, and confidence limits for single-units histograms. Journal of
Neuroscience Methods. 5(4):317-25, 1982
Options
The following options to calculate neuron frequency F are available:
Use all file data. Here T is the total length of experimental session, N is the total number of
spikes for a given neuron.
Use 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 time intervals corresponding to prereference bins. This option only works for a stimulation-
type data. For example, if you stimulate every second and calculate PSTH 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 PSTH or crosscorrelogram time axis minimum
parameter; XMin should be negative). T is the length of all (r+XMin, r) intervals that do not
overlap, N is the number of spikes in these intervals. If more than 5% of intervals overlap, F is
set to zero.
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