A tutorial on hidden Markov models using Stan

We implement a standard Hidden Markov Model (HMM) and the Input-Output Hidden Markov Model for unsupervised learning of time series dynamics in Stan. We begin by reviewing three commonly-used algorithms for inference and parameter estimation, as well as a number of computational techniques and modeling strategies that make full Bayesian inference practical. For both models, we demonstrate the effectiveness of our proposed approach in simulations. Finally, we give an example of embedding a HMM within a larger model using an example from the econometrics literature.