Description Usage Arguments Details Value Note Author(s) References See Also Examples
hist.lockedTrain
constructs and plot.hist.lockedTrain
plots estimates of what Cox and Lewis (1966) call the auto or
crossintensity functions. The autointensity function is also called
the renewal density by Cox and Lewis and by Perkel et al (1967) while
it is called the intensity of the Palm distribution by Ogata
(1988). The (estimate of) the crossintensity function is called
crosscorrelation function by Perkel et al (1967b) and
crosscorrelation histogram by Brillinger et al (1976).
1 2 3 4 5 6 
x 
a 
bw 
a nonnegative numeric, the bin width. 
breaks 
a vector giving the breakpoints between cells. If

plot 
a logical. If 
style 
a character. The style of the plot, 
CI 
a numeric vector with at most two elements. The coverage probability of the confidence intervals. 
unit 
a character. The unit in which the spike times are expressed. 
xlab 
a character. The x label. Default supplied. 
ylab 
a character. The y label. Default supplied. 
xlim 
a numeric. See 
ylim 
a numeric. See 
type 
see 
pch 
see 
... 
see 
The intensity of the Palm distribution (Ogata, 1988, p 13) is estimated by:
m(s) = Prob(event in (t+s,t+s+bw)  event at t) / bw
It is called renewal density by Perkel et al (1967) and defined by their Eq. 10, p 404. Under the null hypothesis of a stationary Poisson process it is a constant whose value is the mean discharge rate.
The crossintensity function of two spike trains A and B is estimated by (Perkel et al, 1967b, p424, Eq. 4 and 5):
m(s;AB) = Prob(B event in (t+s,t+s+bw)  A event at t) / bw
The style
argument of plot.hist.lockedTrain
generates a
plot looking like Fig. 6, p 18 of Ogata (1988) if set to
"Ogata"
. Using style
"Brillinger"
plots the
square root of the estimate.
When argument plot
in hist.lockedTrain
is set to FALSE
a list of class hist.lockedTrain
with the following components is
returned:
density 
the density estimate. Equivalent of the component

breaks 
a numeric vector with the breaks in between which spikes
were counted. Similar to the component of the same name returned by 
mids 
a numeric vector with the mid points of

bw 
the bin width used. 
nRef 
the total number of reference spikes used. 
refFreq 
the mean frequency of the reference neuron. 
testFreq 
the mean frequency of the test neuron. 
obsTime 
the total observation time used (in s). 
CCH 
a logical which is 
call 
the matched call. 
The confidence intervals are obtained from a Poisson distribution with
parameter:
refFreq
* testFreq
* bw
* obsTime
. Once the
quantiles of the Poisson distribution have been obtained they are divided
by: refFreq
* bw
* obsTime
These intervals are valid under the stationary Poisson null hypothesis for the autointensity estimates. They are valid under the stationary independent null hypothesis for the crossintensity. There is NO NEED to assume that the test train is Poisson or renewal. See Perkel et al (1967b) and McFadden (1962) for a justification/proof of that. The square root transform of Brillinger (1976) and Brillinger et al (1976) is (in my opinion) a perfect example of shooting at a sparrow with a bazooka. An oversized method to get at an intuitively obvious result. There is moreover no need to stabilize the variance if your testing against a Poisson with a constant rate since then the variance of the null hypothesis is stable to start with. These (square root) transforms are useful for least square fits with a Poisson noise but NOT in the present context.
Christophe Pouzat christophe.pouzat@gmail.com
Ogata, Yosihiko (1988) Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes. Journal of the American Statistical Association 83: 927.
D. R. Cox and P. A. W. Lewis (1966) The Statistical Analysis of Series of Events. John Wiley and Sons.
J. A. McFadden (1962) On the Lengths of Intervals in a Stationary Point Process. Journal of the Royal Statistical Society. Series B, 24: 364382
Perkel D. H., Gerstein, G. L. and Moore G. P. (1967) Neural Spike Trains and Stochastic Point Processes. I. The Single Spike Train. Biophys. J., 7: 391418. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=4292791
Perkel D. H., Gerstein, G. L. and Moore G. P. (1967b) Neural Spike Trains and Stochastic Point Processes. I. Simultaneous Spike Trains. Biophys. J., 7: 419440. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=4292792
David R. Brillinger, Hugh L. Bryant and Jose P. Segundo (1976) Identification of synaptic interactions. Biol Cybern, 22: 213228.
David R. Brillinger (1976) Estimation of the SecondOrder Intensities of a Bivariate Stationary Point Process. Journal of the Royal Statistical Society. Series B (Methodological), 38, 6066.
varianceTime
,
renewalTestPlot
,
lockedTrain
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  ## Reproduce Fig. 6 of Ogata 1988
data(ShallowShocks)
shalShocks < lockedTrain(as.spikeTrain(ShallowShocks$Date),,c(0,500))
shalShocksH < hist(shalShocks,5,plot=FALSE)
plot(shalShocksH,"Ogata",c(0.95,0.99),xlab="TIME LAG (DAYS)",ylab="NUMBER OF EVENTS PER DAY")
## Reproduce Fig. 7 of Ogata 1988
myBinNb < 101
myMidPoints < seq(from = 1, to = 6, length.out=myBinNb)
myMidPoints < 10^myMidPoints/200
myBreaks < c(0,myMidPoints[myBinNb] + diff(myMidPoints) / 2)
shalShocksH2 < hist(shalShocks,breaks=myBreaks,plot=FALSE)
yy < abs(shalShocksH2$density  shalShocksH2$refFreq)
plot(shalShocksH2$mids[shalShocksH2$density>0],
yy[shalShocksH2$density>0],
pch = 1,
xlim = c(0.001,10000),
log = "xy",
xlab = "TIME LAG (DAYS)",
ylab = "NUMBER OF EVENTS PER DAY"
)

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