NONLINEAR FORECASTING OF SPIKE TRAINS FROM SENSORY NEURONS

The sequence of firing times of a neuron can be viewed as a point process. The problem of spike train analysis is to infer the underlying neural dynamics from this point process when, for example, one does not have access to a state variable such as intracellular voltage. Traditional analyses of spike trains have focussed to a large extent on fitting the parameters of a model stochastic point process to the data, such as the intensity of a homogeneous Poisson point process. This paper shows how methods from nonlinear time series analysis can be used to gain knowledge about correlations between the spiking events recorded from periodically driven sensory neurons. Results on nonlinear forecastability of these spike trains are compared to those on data sets derived from the original data set and satisfying an appropriately chosen null hypothesis. While no predictability, linear or nonlinear, is revealed by our analysis of the raw data using local linear predictors, it appears that there is some predictability in the successive phases (rather than intervals) at which the neurons fire.