A theoretical basis for conditional probability analyses of neural discharge activity

A theory has been developed which allows the estimation of the probability density of a discharge, given that an arbitrary condition is fulfilled. It is shown that the common methods for the evaluation of a post-stimulus time (PST) histogram and a hazard function can be considered as special applications of this theory. Whereas the usual hazard function shows how the probability of a discharge depends on the time elapsed since the last discharge, generalized hazard functions proposed in the present paper allow to reveal also the influence of the last but one discharge, the last but two discharge, and so on. In contrast to the usual method for the estimation of a hazard function, the applicability of the procedures proposed here is not restricted to stationary discharge activity. Some elementary applications are illustrated by analysing simulated discharge activity mimicing the response of a single auditory-nerve fiber to a high-intensity tone burst.