# Multitaper Analysis of Evolutionary Spectra from Multivariate Spiking Observations

## TL;DR

This paper introduces a multitaper spectral estimation method for analyzing the evolutionary spectra of latent non-stationary processes from multivariate neural spiking data, improving bias-variance trade-offs.

## Contribution

We develop a novel multitaper spectral estimation technique tailored for multivariate spiking observations, with theoretical bias-variance bounds and demonstrated superior performance.

## Key findings

- Significant bias-variance trade-off improvements over existing methods
- Theoretical bounds on estimator bias and variance
- Successful application to real neural spiking data

## Abstract

Extracting the spectral representations of the neural processes that underlie spiking activity is key to understanding how the 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 a challenging problem. 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 evolutionary spectral density of the latent non-stationary processes that drive spiking activity, based on point process theory. We establish theoretical bounds on the bias-variance trade-off of the proposed estimator. Finally, we compare the performance of our proposed technique with existing methods using simulation studies and application to real data, which reveal significant gains in terms of the bias-variance trade-off.