Albert and Le, Leroux and Puterman describe the fitting of two-state Poisson–HMMs to series of daily counts of epileptic seizures in one patient. The models appear to be a promising tool for the analysis of seizure counts, the more so as there are suggestions in the neurology literature that the susceptibility of a patient to seizures may vary in a fashion that can reasonably be represented by a Markov chain. Le et al. use an HMM of the type described by Leroux and Puterman. Their model does not assume that the underlying Markov chain is stationary. This chapter considers a similar HMM, but based on a stationary Markov chain and fitted by maximization of the unconditional likelihood of the observations.