  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.
