The analysis of neuronal discharge sequences: change-point estimation and comparison of variances

A key problem in neurophysiology is to determine whether, after presentation of a stimulus, there has been a modification in the discharge of a recorded neuron and if so, an attempt is made to estimate the latency of the response. The estimation problem can be considered as that of the estimation of a change-point in a sequence of random variables. The gamma distribution is adequate to model the distribution of intervals between action potentials for different types of neurons. Simulations show that the maximum likelihood estimator based on this model is efficient and robust. An additional problem, in the case of experiments in which a movement follows the stimulus, is to determine whether a response is related to the stimulus or to the movement. A test based on the comparison of marginal scales of a bivariate distribution is proposed. The whole procedure has been tested in simulation and with real examples.