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

TL;DR

This paper introduces a Bayesian spline-based hidden Markov model that flexibly models complex data, automatically determines the number of states, and is demonstrated on animal activity and sleep data, showing superior performance.

Contribution

It presents a novel Bayesian framework with B-spline emission distributions and trans-dimensional sampling for model selection, improving over existing methods.

Findings

Outperforms alternative approaches in simulations

Robustness and scalability demonstrated

Effective in animal activity 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.