Bayesian inference for spline-based hidden Markov models

Authors:
  • BRBärbel Finkenstädt Rand
    Bärbel Finkenstädt Rand
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Abstract
B-spline-based hidden Markov models (HMMs), where the emission densities are specified as mixtures of normalized B-spline basis functions, offer a more flexible modelling approach to data than conventional parametric HMMs. We introduce a fully Bayesian framework for inference in these nonparametric models where the number of states may be unknown along with other model parameters. We propose the use of a trans-dimensional Markov chain inference algorithm to identify a parsimonious knot configuration of the B-splines while model selection regarding the number of states can be performed within a parallel sampling framework. The feasibility and efficiency of our proposed methodology is shown in a simulation study. Its explorative use for real data is demonstrated for activity acceleration data in animals, i.e. whitetip-sharks. The flexibility of a Bayesian approach allows us to extend the modelling framework in a straightforward way and we demonstrate this by developing a hierarchical conditional HMM to analyse human accelerator activity data to focus on studying small movements and/or inactivity during sleep.

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