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

Abstract: B-spline-based hidden Markov models employ B-splines to specify the emission distributions, offering a more flexible modelling approach to data than conventional parametric HMMs. We introduce a Bayesian framework for inference, enabling the simultaneous estimation of all unknown model parameters including the number of states. A parsimonious knot configuration of the B-splines is identified by the use of a trans-dimensional Markov chain sampling algorithm, while model selection regarding the number of states can be performed based on the marginal likelihood within a parallel sampling framework. Using extensive simulation studies, we demonstrate the superiority of our methodology over alternative approaches as well as its robustness and scalability. We illustrate the explorative use of our methods for data on activity in animals, i.e. whitetip-sharks. The flexibility of our Bayesian approach also facilitates the incorporation of more realistic assumptions and we demonstrate this by developing a novel hierarchical conditional HMM to analyse human activity for circadian and sleep modelling.