Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity, but contemporary experiments often use time-varying stimuli and produce time-varying neural responses. More recently, many statistical methods have been developed for nonstationary neural point process data. There has also been much interest in identifying synchrony, meaning events across two or more neurons that are nearly simultaneous at the time scale of the recordings. A natural statistical approach is to discretize time, using short time bins, and to introduce loglinear models for dependency among neurons, but previous use of loglinear modeling technology has assumed stationarity. We introduce a succinct yet powerful class of time-varying loglinear models by (a) allowing individual-neuron effects (main effects) to involve time-varying intensities; (b) also allowing the individual-neuron effects to involve autocovariation effects (history effects) due to past spiking, (c) assuming excess synchrony effects (interaction effects) do not depend on history, and (d) assuming all effects vary smoothly across time. Using data from the primary visual cortex of an anesthetized monkey, we give two examples in which the rate of synchronous spiking cannot be explained by stimulus-related changes in individual-neuron effects. In one example, the excess synchrony disappears when slow-wave “up” states are taken into account as history effects, while in the second example it does not. Standard point process theory explicitly rules out synchronous events. To justify our use of continuous-time methodology, we introduce a framework that incorporates synchronous events and provides continuous-time loglinear point process approximations to discrete-time loglinear models.
"Assessment of synchrony in multiple neural spike trains using loglinear point process models." Ann. Appl. Stat. 5 (2B) 1262 - 1292, June 2011. https://doi.org/10.1214/10-AOAS429