Hierarchical Bayesian spectral analysis of multiple stationary time series

2025-11-24

AI Summary

This paper addresses the challenge of jointly modeling power spectra of multiple stationary time series with heterogeneous lengths. We propose Hierarchical Bayesian Estimation of Spectra (HBEST), a novel hierarchical Bayesian method that simultaneously captures individual spectral specificity and shared population-level structure via global–local coefficient decomposition and truncated cosine basis expansion—enabling interpretable cross-series information sharing and adaptive regularization. HBEST employs a hierarchical prior on log-spectra, a shrinkage-inducing hyperprior, and an MCMC inference framework to robustly mitigate estimation bias arising from spectral variability and length heterogeneity. Simulation studies demonstrate that HBEST achieves significantly higher accuracy and robustness than state-of-the-art methods. Applied to real heart rate variability data, HBEST successfully identifies frequency-band features significantly associated with cardiovascular risk factors—including hypertension and age—validating its practical utility in physiological signal analysis.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Estimating power spectra for multiple biomedical time series
• Addressing spectral variability and varying time series lengths
• Providing hierarchical Bayesian framework for population and individual analysis

Innovation

• Hierarchical Bayesian framework for multiple time series
• Global-local coefficient decomposition in basis expansion
• Shrinkage priors enabling regularized spectral estimation