Single molecule spectroscopy experiments and molecular dynamics simulations have several profound features in common, chief among which is that both follow the dynamics of some degrees of freedom of a single molecule over time. The analysis is essentially the same: one investigates the changes in the degrees of freedom followed. For instance, in a single molecule fluorescence experiment, the degree of freedom is often the number of photons detected in some time period. In this article, we introduce a straightforward Bayesian method for detecting if and when changes Occurred. In contrast to methods based upon maximum likelihood estimates, a Bayesian approach allows for a more systematic means not only to change point detection but also to cluster the data into states. Most importantly, the Bayesian method Supplies a simpler hypothesis testing framework. Although we focus oil Poisson-distributed data, the Bayesian methods outlined here can in principle be applied to data sampled from any distribution.