Marginal Parametrizations for Hidden Markov Models

We propose to parameterize the two components of a hidden Markov model (HMM), the observation model and the latent model, using the marginal parameterization (Bergsma and Rudas, 2002, Bartolucci {\it et al.}, 2009). We will show that many interesting hypotheses on the probabilities of the observable variables given the latent states and on the transition probabilities of the latent processes of the HMM can be verified by testing constraints on marginal parameters.