We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model, assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a transdimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.
Bibliographical noteFunding Information:
Funding. B. Hadj-Amar was supported by the Oxford-Warwick Statistics Programme (OxWaSP) and the Engineering and Physical Sciences Research Council (EPSRC), Grant Number EP/L016710/1. R. Huckstepp was supported by the Medical Research Council (MRC), Grant Number MC/PC/15070.
© Institute of Mathematical Statistics, 2021.
- Bayesian nonparametrics
- Hierarchical Dirichlet process
- Reversible-jump MCMC
- Sleep apnea
- Time-varying frequencies
PubMed: MeSH publication types
- Journal Article