STAR (version 0.3-7)

varianceTime: Variance-Time Analysis for Spike Trains

Description

Performs Variance-Time Analysis for a Spike Train (or any univariate time series) assuming a Poisson Process with the same Rate as the Spike Train.

Usage

varianceTime(spikeTrain, CI = c(0.95, 0.99), windowSizes)
is.varianceTime(obj)
"plot"(x, style = c("default", "Ogata"), unit = "s", xlab, ylab, main, sub, xlim, ylim, ...)

Arguments

spikeTrain

a spikeTrain object or a vector which can be coerced to such an object.

obj

a object to test against a varianceTime object.

x

a varianceTime object.

CI

a numeric vector with at most two elements. The coverage probability of the confidence intervals.

windowSizes

a numeric increasing vector of positive numbers. The window sizes used to split the spike train.

style

a character. The style of the plot, "default" or "Ogata".

unit

a character. The unit in which the spike times are expressed.

xlab

a character. The x label.

ylab

a character. The y label.

main

a character. The title.

sub

a character. The subtitle.

xlim

a numeric. See plot.

ylim

a numeric. See plot.

...

see plot.

Value

varianceTime returns a list of class varianceTime with the following elements:

s2

numeric vector of empirical variance.

sigma2

numeric vector of expected variance under the Poisson hypothesis.

ciUp

a numeric vector or a 2 rows matrix with the upper limits of the confidence interval(s).

ciLow

a numeric vector or a 2 rows matrix with the lower limits of the confidence interval(s).

windowSizes

numeric vector of window sizes actually used.

CI

a numeric vector, the coverage probabilities of the confidence intervals.

call

the matched call

plot.varianceTime is used for its side effect: a graph is produced.is.varianceTime returns TRUE if its argument is a varianceTime object and FALSE otherwise.

Details

See Fig. 5 of Ogata (1988) for details. The confidence intervals are obtained with a Normal approximation of the Poisson distribution.

References

Ogata, Yosihiko (1988) Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes. Journal of the American Statistical Association 83: 9-27.

See Also

acf.spikeTrain, renewalTestPlot

Examples

## Replicate (almost) Fig. 5 of Ogata 1988
data(ShallowShocks)
vtShallow <- varianceTime(ShallowShocks$Date,,c(5,10,20,40,60,80,seq(100,500,by = 25))*10)
is.varianceTime(vtShallow)
plot(vtShallow, style="Ogata")