**Can Cai, Robert E. Kass, and Valérie Ventura**

The joint peristimulus time histogram (JPSTH) provides a visual
representation of the dynamics of correlated activity for a
pair of neurons. There are many ways to adjust the JPSTH
for the time-varying firing-rate modulation
of each neuron, and then to define a suitable measure of
time-varying correlated activity.
Our approach is to introduce a statistical model for the time-varying
joint spiking activity so that
the joint firing rate can be estimated more efficiently.
We have applied an adaptive smoothing method, which
has been shown to be effective in capturing sudden changes in firing
rate, to the
ratio of joint firing probability to the probability of firing
predicted by independence.
A Bootstrap procedure, applicable to
both Poisson and non-Poisson data, was used to define
a statistical significance test of
whether a large ratio could be due to chance alone.
A numerical simulation showed that the Bootstrap-based
significance test has very nearly the correct rejection probability,
and can have markedly better power to detect
departures from independence than does an approach based
on testing contiguous bins in the JPSTH.
In a companion paper (Cai *et al.* 2004b)
we show how this formulation can accommodate latency and time-varying
excitability effects, which can confound spike timing effects.

*Keywords:* Bootstrap, Correlation, Cross-correlogram,
Excursion significance test,
Firing rate,
Gamma process,
IMI process,
Non-Poisson Spiking,
Peri-Stimulus Time Histogram,
Point Process,
Smoothing,
Statistical model,
Spike Train Analysis

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