Bayesian Nonparametric Estimation of the Spectral Density Function, with Applications to Spectral Analysis of EEG Data

• Activity Number: 536 - Contributed Poster Presentations: Section on Statistics in Imaging
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Guillermo Cuauhtemoctzin Granados Garcia* and Hernando Ombao and Mark Fiecas
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology and University of Minnesota
• Keywords: Spectral density estimation; Bayesian nonparametric models; EEG analysis; Dirichlet process

Abstract

The goal of this project is to develop a nonparametric Bayesian method for estimating the spectrum of a stationary time series using data collected from neuroscience experiments. Our approach is to represent the spectral density function as a probability density function, which we model, using a mixture of beta densities with random weights with a Dirichlet process prior. This approach gives rise to a nonparametric Bayesian method for spectral density estimation. We use Markov Chain Monte Carlo to simulate the spectral density, which allows us to obtain point estimates and statistics of interest such as credible intervals and posterior quantities. We validate our model using numerical experiments, by testing the model with time series generated from a random walk with drift, as well as, an ARMA model. We give an empirical illustration of this modeling approach by conducting spectral analysis on brain activity measured by an electroencephalogram. The spectrum is estimated in order to identify the main frequency bands of activity of the brain. Finally, we discuss future work that extends the model to several dimensions.