In this work, we develop a fully Bayesian method for the calculation of probability distributions of single-exponential rates for any single-molecule process. These distributions can even be derived when no transitions from one state to another have been observed, since in that case the data can be used to estimate a lower bound on the rate. Using a Bayesian hypothesis test, one can easily test whether a transition occurs at the same rate or at different rates in two data sets. We illustrate these methods with molecular dynamics simulations of the folding of a beta-sheet protein. However, the theory presented here can be used on any data from simulation or experiment for which a two-state description is appropriate.