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B-spline-based hidden Markov models employ B-splines to specify the emissiondistributions, offering a more flexible modelling approach to data thanconventional parametric HMMs. We introduce a Bayesian framework for inference,enabling the simultaneous estimation of all unknown model parameters includingthe number of states. A parsimonious knot configuration of the B-splines isidentified by the use of a trans-dimensional Markov chain sampling algorithm,while model selection regarding the number of states can be performed based onthe marginal likelihood within a parallel sampling framework. Using extensivesimulation studies, we demonstrate the superiority of our methodology overalternative approaches as well as its robustness and scalability. We illustratethe explorative use of our methods for data on activity in animals, i.e.whitetip-sharks. The flexibility of our Bayesian approach also facilitates theincorporation of more realistic assumptions and we demonstrate this bydeveloping a novel hierarchical conditional HMM to analyse human activity forcircadian and sleep modelling.

Bayesian spline-based hidden Markov models with applications to actimetry data and sleep analysis