Patching With Sequential Updating for High-Fidelity Bayesian Spectral Estimation of Physiological Time Series

Physiological time series reflect the underlying behavior of physiological systems. In this paper, we introduce a novel patching with sequential updating for Bayesian nonparametric spectral estimation (PBNSE) to enhance spectral estimation and interpretation of imperfect physiological time series with fragmented, noncontiguous segments. PBNSE incorporates four key strategies: (1) modeling patches as patch-specific Gaussian processes (GPs); (2) patch-dependence, where each patch involves a joint GP with a shared kernel, capturing both observation and spectral dependencies across all patches; (3) sequential parameter shift that transfers knowledge between patches while maintaining computational traceability; and (4) aggregating patch-level posterior spectra into a unified power spectral density (PSD) estimate and computing the expectation of the PSD in a closed form. Extensive experiments demonstrate significant improvements in spectral accuracy and robustness compared to state-of-the-art methods such as BNSE, multitaper, periodogram, Lomb-Scargle, functional kernel learning (FKL), and variational sparse spectrum (SVSS). PBNSE addresses key challenges in physiological signal analysis, including irregular sampling, incomplete signal, and varying noise. The widespread adoption of PBNSE in physiological signal research has the potential to enhance the accuracy of spectral estimation and improve the robustness of interpreting complex, real-world physiological time series.