Bayesian Nonparametric Multivariate Mixture of Autoregressive Processes with Application to Brain Signals

Abstract

One of neuroscience’s goals is to study the interactions between different brain regions during rest and while performing specific cognitive tasks. Multivariate Bayesian autoregressive decomposition (MBMARD) is proposed as an intuitive and novel Bayesian non-parametric model to represent high-dimensional signals as a low-dimensional mixture of univariate uncorrelated latent oscillations. Each latent oscillation captures a specific underlying oscillatory activity and, hence, is modeled as a unique second-order autoregressive process due to a compelling property, namely, that its spectral density’s shape is characterized by a unique frequency peak and bandwidth, parameterized by a location and a scale parameter. The posterior distributions of the latent oscillation parameters are computed using a Metropolis-within-Gibbs algorithm. One of the advantages of the MBMARD model is its higher robustness against misspecification, compared with standard models. The main scientific questions addressed by the MBMARD model relate to the effects of long-term alcohol abuse on memory. These effects were examined by analyzing the electroencephalogram records of alcoholic and non-alcoholic subjects performing a visual recognition experiment. The MBMARD model yielded novel and interesting findings, including the identification of subject-specific clusters of low- and high-frequency oscillations in different brain regions.