As alternative to the frequentist approach, one can also consider Bayesian estimation. There are several approaches to Bayesian inference in hidden Markov models. This chapter demonstrates an application of Bayesian inference to Poisson–HMMs. There are obstacles to be overcome, such as label switching and the difficulty of estimating m, the number of states, and some of these are model specific. In the Bayesian approach to model selection, the number of states, m, is a parameter whose value is assessed from its posterior distribution. It is clear from the comparison of two independent runs of the harmonic mean estimator (left panel) that it is indeed very unstable. In the first run it would have chosen a three-state model by a large margin, and in the second run a four-state model.