Circular insights for rhythmic health: A Bayesian approach with stochastic diffusion for characterizing human physiological rhythms with applications to arrhythmia detection

Accurate detection of arrhythmic patterns in physiological signals-particularly electrocardiogram (ECG)-is vital for early diagnosis and intervention. Traditional amplitude-based models often fail to capture disruptions in the underlying phase dynamics. In this study, we propose a novel Bayesian framework based on circular stochastic differential equations (SDEs) to model the temporal evolution of cardiac phase as a diffusion process on the circle. Using the MIT-BIH arrhythmia dataset, and also based on extensive simulation of ECG signals with phase anomalies, we validate the proposed methodology and compare our method against two standard approaches: a linear autoregressive (AR) model and a Fourier-based spectral method. Quantitative evaluation demonstrates that depending on the assumption, our method capable of achieving superior accuracy while better balancing sensitivity and specificity in detecting subtle phase anomalies, particularly those undetectable by conventional amplitude-based tools. Unlike existing techniques, our framework is naturally suited for circular data and offers short-term probabilistic prediction. The proposed approach provides a statistically coherent and interpretable framework for modeling rhythmic biomedical signals, laying a foundation for future extensions to multimodal or hierarchical physiological models.