Bootstrap significance test of synchronous spike events--a case study of oscillatory spike trains

The purpose of this monograph is two folds. Firstly, we introduce challenging spike data to the statistical analysis. The data of two neurons recorded from the cat visual pathway show various non-stationary characteristics not fitted by the Poisson spike train. Spike firings of both neurons are strongly periodic and tightly synchronized. Our second purpose is a case study of applications of various statistical methods for the significance test of the time-varying spike synchrony. We provide various general remarks to the statistical analysis of the synchronous spike activities. At first, we apply the unitary event analysis. The significance limit for the coincident spike events by the Poisson distribution is compared with the limit given by the non-parametric test based on the bootstrap samplings. The bootstrap test performs superior to the Poisson test in two respects: (1) avoids false positives due to the sudden change of spike density; and (2) takes into account the non-stationary change of the spiking pattern at different sampling windows. When the spike trains are highly periodic, the histogram of the number of accidental coincident spike events over the bootstrap samples has a systematically larger variance than the Poisson distribution. We find that a large variance originates from the correlation between the successive coincident spike events in the structured spike trains. The significance of the time-varying synchrony is tested by another statistical method by Ventura et al., which is based on the adaptive smoothing method and the bootstrap significance test. .