AI 中文总结
针对时间序列数据频谱分析，提出贝叶斯尖峰平板框架，结合频率选择与降维，通过随机搜索算法探索后验空间，扩展到多元信号。模拟及实际数据应用表明该方法在频率估计等方面性能优越，适用性广。
AI 中文摘要
本文介绍了一种用于时间序列数据频谱分析的贝叶斯尖峰平板框架。该方法将频率选择和降维与精细的候选频率网格相结合，通过结构化的尖峰平板先验实现振荡成分的高分辨率恢复并促进稀疏性。一种随机搜索算法有效探索后验空间，得出量化每个频率相关性的后验包含概率。通过频率包含模式的分层先验将框架扩展到多元信号。模拟研究表明该方法在频率估计和谱功率重建方面比现有方法更稳健、性能更优。在癫痫和健康个体数据应用中均有良好表现，建立了强大且可解释的谱分析方法。
英文摘要
This paper introduces a Bayesian spike-and-slab framework for spectral analysis of time series data. The proposed method combines frequency selection and dimensionality reduction with a refined grid of candidate frequencies, enabling high-resolution recovery of oscillatory components while promoting sparsity through a structured spike-and-slab prior. A stochastic search algorithm efficiently explores the posterior space, yielding posterior inclusion probabilities that quantify the relevance of each frequency. We extend the framework to multivariate signals via a hierarchical prior on frequency inclusion patterns, allowing the model to capture both shared and component-specific rhythms across multiple time series. Extensive simulation studies demonstrate the method's robustness and superior performance in frequency estimation and spectral power reconstruction compared to existing approaches. Applied to actigraphy data from individuals with partial-onset seizures, the univariate model identifies clinically relevant circadian and ultradian rhythms. In a second application, for the joint analysis of physical activity and skin temperature from a healthy individual, the multivariate model reveals partially overlapping rhythmic components consistent with known physiological coupling. This work establishes a powerful and interpretable approach to spectral analysis, with broad applicability to wearable data, chronobiology, and personalized health monitoring.
CommentsAccepted for publication in the Annals of Applied Statistics
