Regression spline model for neural spike train data

Neuroscience experiments and neural spike train data have special features that present novel and exciting challenges for statistical researches. Several standard statistical procedures, widely used in other fields of science, have found their way into mainstream application in neuroscience data analysis. Given the firing times of an ensemble of neurons and their stimulating and inhibitory inputs from several regions, an integrated model is introduced based on the conditional intensity function approach. This is different from the existing methods where the intensity function is approximated by discretization with the sampling intervals chosen arbitrarily. In

a a tensor product of splines for the peer or predictor spike trains. The parameters are defined by those used in constructing the polynomial splines, and they will be estimated by the maximum likelihood method. The statistical properties of this procedure will be evaluated using both a simulated experiment and a real data set involving 15 peers of neural spike trains. Our model captures the underlying spontaneous firing of the target as well as the stimulus inputs from its peers, both in continuous time.