Frequency Selection in Bayesian Spectral Modeling of Time Series Data with Applications to Wearable Device Measurements
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.