In many medical experiments data are collected across time, over a number of similar trials or a number of experimental units. As is the case of neural spike train studies, these data may be in the form of counts of events per unit of time. These counts may be correlated within each trial. It is often of interest to know if the introduction of an intervention, such as the application of a stimulus, affects the distribution of the counts over the course of the experiment. In such investigations, each trial generates a sequence of data which may or may not contain a change in distribution at some point in time. Each sequence of integer counts can be viewed as arising from a Poisson process and are therefore independently distributed, or as an integer valued time series that allows for correlations between these counts. The main aim of this paper is to show how the ensemble of sample paths may be used to make inference about the distribution of the instantaneous times of change in a given population. This will be accomplished using a Bayesian hierarchical model for these change-points in time. A bonus of these models is they also allow for inference about the probability of a change in each unit, and the magnitude of the effects, if any. The use of such change-point models on integer-valued time series is illustrated here on neural spike train data, although the methods can be applied to other situations where integer-valued processes arise.