The power spectrum of biomedical time series provides important indirect measurements of physiological processes underlying health and biological functions. However, simultaneously characterizing power spectra for multiple time series remains challenging due to extra spectral variability and varying time series lengths. We propose a method for hierarchical Bayesian estimation of stationary time series (HBEST) that provides an interpretable framework for efficiently modeling multiple power spectra. HBEST models log power spectra using a truncated cosine basis expansion with a novel global-local coefficient decomposition, enabling simultaneous estimation of population-level and individual-level power spectra and accommodating time series of varying lengths. The fully Bayesian framework provides shrinkage priors for regularized estimation and efficient information sharing. Simulations demonstrate HBEST's advantages over competing methods in computational efficiency and estimation accuracy. An application to heart rate variability time series demonstrates HBEST's ability to accurately characterize power spectra and capture associations with traditional cardiovascular risk factors.

翻译：生物医学时间序列的功率谱为健康与生物功能背后的生理过程提供了重要的间接测量。然而，由于额外的谱变异性和时间序列长度的差异，同时表征多个时间序列的功率谱仍然具有挑战性。我们提出了一种用于平稳时间序列的层次贝叶斯估计方法（HBEST），该方法为高效建模多个功率谱提供了一个可解释的框架。HBEST使用截断余弦基展开对对数功率谱进行建模，并采用一种新颖的全局-局部系数分解，能够同时估计群体水平和个体水平的功率谱，并适应不同长度的时间序列。该完全贝叶斯框架提供了收缩先验以实现正则化估计和高效的信息共享。仿真实验表明，HBEST在计算效率和估计精度方面优于竞争方法。在心率变异性时间序列的应用中，HBEST展示了其准确表征功率谱并捕捉与传统心血管风险因素关联的能力。