A Bayesian multitaper method for nonstationary data with application to EEG analysis

Nonparametric spectral analysis using overlapping sliding windows is among the most widely used techniques in analyzing nonstationary time series. Although sliding window analysis is convenient to implement, the resulting estimates are sensitive to the subjective choice of window length and overlap extent and additionally lack precise statistical interpretation. In this paper, we propose a spectral estimator by explicitly modeling the spectral dynamics through combining the multitaper method with state-space models in a Bayesian estimation framework. The states are efficiently estimated using an instance of the Expectation-Maximization algorithm, from which the spectral estimates and their confidence intervals are constructed. We apply our proposed algorithm to synthetic data as well as real data from human EEG recordings, revealing significant improvements in spectral resolution and noise rejection.