Multitaper Analysis of Semi-Stationary Spectra from Multivariate Neuronal Spiking Observations

Extracting the spectral representations of neural processes that underlie spiking activity is key to understanding how brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied, inferring the spectral representation of latent non-stationary processes based on spiking observations is challenging due to the underlying nonlinearities that limit the spectrotemporal resolution of existing methods. In this paper, we address this issue by developing a multitaper spectral estimation methodology that can be directly applied to multivariate spiking observations in order to extract the semi-stationary spectral density of the latent non-stationary processes that govern spiking activity. We establish theoretical bounds on the bias-variance trade-off of our proposed estimator. Finally, application of our proposed technique to simulated and real data reveals significant performance gains over existing methods.