A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspi ke interval difference (JISID) analysis. By design, this method detects cha nges 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 se rial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint d istribution of consecutive changes in ISIs, from which the serial dependenc e of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint di stribution of consecutive ISI differences (ISIDs) is quantified. The graphi cal location of points in the JISID scatter plot reveals the local trends i n firing (i.e., monotonically increasing, monotonically decreasing, or tran sitional firing). The trajectory of these points in the serial-JISID plot t races 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 patter n. We provide complete theoretical interpretations of the JISID analysis. W e also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons.