Identifying the recurrence of sleep apnea using a harmonic hidden Markov model

Abstract

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 trans-dimensional 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. Keywords and phrasesSleep Apnea; Time-Varying Frequencies; Reversible-Jump MCMC; Bayesian Non-parametrics; Hierarchical Dirichlet process 1 GEM is an abbreviation for Griffiths, Engen and McCloskey, see Ignatov (1982); Perman, Pitman and Yor (1992); Pitman (1996) for background.

Statistical analysis of multi‐day solar irradiance using a threshold time series model

“…Remark Regime models can also be estimated using the oscillatory properties. For example Hadj‐Amar et al (2021) fitted a HMM assuming that periodicity characterized each regime. We could use a combination between these ideas and Whittle likelihood to develop an alternative inference procedure.…”

Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity

“…VAR models have proven to be especially useful in applications to complex data, for example in the analysis of the dynamical behaviours of economic and financial time series (Watson, 1994;Ahelegbey et al, 2016;Kalli and Griffin, 2018), and of high-dimensional signals arising from different areas of the brain, such as fMRI (Goebel et al, 2003) and EEG data (Prado et al, 2006;Kammerdiner and Pardalos, 2010). Nonstationarity is commonly observed in many physiological time series, as a result of external perturbations or due to an individual performing distinct tasks or experiences (Ombao et al, 2018;Hadj-Amar et al, 2021). In the application of this paper, we consider multivariate time series data that arise from a study on human gesture phase segmentation based on sensor data.…”