Noise-Robust Phase Connectivity Estimation via Bayesian Circular Functional Models (2509.06418v1)

Abstract: The phase locking value (PLV) is a widely used measure to detect phase connectivity. Main drawbacks of the standard PLV are it can be sensitive to noisy observations and does not provide uncertainty measures under finite samples. To overcome the difficulty, we propose a model-based PLV through nonparametric statistical modeling. Specifically, since the discrete time series of phase can be regarded as a functional observation taking values on circle, we employ a Bayesian model for circular-variate functional data, which gives denoising and inference on the resulting PLV values. The proposed model is defined through "wrapping" functional Gaussian models on real line, for which we develop an efficient posterior computation algorithm using Gibbs sampler. The usefulness of the proposed method is demonstrated through simulation experiments based on real EEG data.