  Hidden Markov models (HMMs) offer a robust and efficient framework for
analyzing time series data, modelling both the underlying latent state
progression over time and the observation process, conditional on the latent
state. However, a critical challenge lies in determining the appropriate number
of underlying states, often unknown in practice. In this paper, we employ a
Bayesian framework, treating the number of states as a random variable and
employing reversible jump Markov chain Monte Carlo to sample from the posterior
distributions of all parameters, including the number of states. Additionally,
we introduce repulsive priors for the state parameters in HMMs, and hence avoid
overfitting issues and promote parsimonious models with dissimilar state
components. We perform an extensive simulation study comparing performance of
models with independent and repulsive prior distributions on the state
parameters, and demonstrate our proposed framework on two ecological case
studies: GPS tracking data on muskox in Antarctica and acoustic data on Cape
gannets in South Africa. Our results highlight how our framework effectively
explores the model space, defined by models with different latent state
dimensions, while leading to latent states that are distinguished better and
hence are more interpretable, enabling better understanding of complex dynamic
systems.
