A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing...

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons.