varianceTime: Variance-Time Analysis for Spike Trains

In STAR: Spike Train Analysis with R

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)
## S3 method for class 'varianceTime'
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.

Details

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

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.

Author(s)

Christophe Pouzat [e-mail] and Chong Gu [e-mail] for a correction on the sampling variance of the variance of a normal 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")

STAR documentation built on May 2, 2019, 11:44 a.m.