Hadj-Amar Beniamino, Finkenstädt Bärbel, Fiecas Mark, Huckstepp Robert
Department of Statistics, University of Warwick.
School of Public Health, Division of Biostatistics, University of Minnesota.
Ann Appl Stat. 2021 Sep;15(3):1171-1193. doi: 10.1214/21-AOAS1455.
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.
我们建议通过隐马尔可夫模型对时变周期和振荡过程进行建模，其中状态是通过周期状态的频谱特性来定义的。状态数量以及相关周期均未知，其作用和数量可能因状态而异。我们通过贝叶斯非参数隐马尔可夫模型来解决这个推理问题，该模型假设不同状态之间的切换动态服从粘性分层狄利克雷过程，同时通过跨维马尔可夫链蒙特卡罗采样步骤来探索表征每个状态的周期。我们开发了完整的贝叶斯推理算法，并说明了我们提出的方法在不同模拟研究中的应用，以及与呼吸研究相关的应用，该研究专注于检测人类呼吸轨迹中的呼吸暂停实例。
