  The study of animal behavioural states inferred through hidden Markov models
and similar state switching models has seen a significant increase in
popularity in recent years. The ability to account for varying levels of
behavioural scale has become possible through hierarchical hidden Markov
models, but additional levels lead to higher complexity and increased
correlation between model components. Maximum likelihood approaches to
inference using the EM algorithm and direct optimisation of likelihoods are
more frequently used, with Bayesian approaches being less favoured due to
computational demands. Given these demands, it is vital that efficient
estimation algorithms are developed when Bayesian methods are preferred. We
study the use of various approaches to improve convergence times and mixing in
Markov chain Monte Carlo methods applied to hierarchical hidden Markov models,
including parallel tempering as an inference facilitation mechanism. The method
shows promise for analysing complex stochastic models with high levels of
correlation between components, but our results show that it requires careful
tuning in order to maximise that potential.
