Spike train ($n(t)={\sum }_i\delta (t-t_i)$)

A sequence of action potential times, represented mathematically as a point process or a sum of Dirac deltas. Its event counts, intervals and correlations summarize different aspects of neural activity.

An interspike interval is the elapsed time between consecutive action potentials in a spike train. Its probability distribution and dependence on previous activity can reveal a neuronal refractory period even when the average firing rate is unchanged.

For a correctly specified conditional rate, transformed interspike intervals have independent unit-exponential distributions, apart from observation-boundary censoring. Their transforms $1-e^{-z_i}$ should be uniform. Distributional checks and serial-correlation checks assess a fitted spike model on held-out data. A history-dependent model must include past spikes in its conditional rate; stimulus-only Poisson spike-train likelihood fitting cannot automatically capture refractoriness.