Identifying the recurrence of sleep apnea using a harmonic hidden Markov model. (English) Zbl 1478.62326

Hadj-Amar, Beniamino; Finkenstädt, Bärbel; Fiecas, Mark; Huckstepp, Robert

Ann. Appl. Stat. 15, No. 3, 1171-1193 (2021).

Summary: 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62M05	Markov processes: estimation; hidden Markov models
62G05	Nonparametric estimation

Keywords:

sleep apnea; time-varying frequencies; reversible-jump MCMC; Bayesian nonparametrics; hierarchical Dirichlet process

Software:

BayesDA; astsa; Label.switching; tsbridge; BayesSpec; PRMLT

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