# Statistical Assessment of Time-Varying Dependence Between Two Neurons

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.