Bayesian Model Search for Nonstationary Periodic Time Series

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behavior. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behavior in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces. Supplementary materials for this article are available online.

本文提出一种新颖的贝叶斯分析方法，用于处理具有振荡特性的非平稳时间序列。我们采用带有未知周期的分段振荡模型对目标时间序列进行近似建模，研究目标为同时估计序列变点，并识别数据中可能随时间演化的周期成分。所提方法基于跨维马尔可夫链蒙特卡洛（trans-dimensional Markov chain Monte Carlo）算法，能够同时更新变点以及各相邻分段对应的周期参数。我们通过两个与电子健康（e-Health）及睡眠研究相关的应用场景验证了所提方法的有效性：一是可识别夜间休息时段人体皮肤温度中的超昼夜振荡现象，二是可从体积描记法记录的呼吸轨迹中检测睡眠呼吸暂停事件。本文配套补充材料可在线获取。