Brain Waves Analysis Via a Non-parametric Bayesian Mixture of Autoregressive Kernels

The standard approach to analyzing brain electrical activity is to examine the spectral density function (SDF) and identify predefined frequency bands that have the most substantial relative contributions to the overall variance of the signal. However, a limitation of this approach is that the precise frequency and bandwidth of oscillations vary with cognitive demands. Thus they should not be arbitrarily defined a priori in an experiment. In this paper, we develop a data-driven approach that identifies (i) the number of prominent peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks). We propose a Bayesian mixture auto-regressive decomposition method (BMARD), which represents the standardized SDFas a Dirichlet process mixture based on a kernel derived from second-order auto-regressive processes which completely characterize the location (peak)and scale (bandwidth) parameters. We present a Metropolis-Hastings within Gibbs algorithm to sample from the posterior distribution of the mixture parameters. Simulation studies demonstrate the robustness and performance of the BMARD method. Finally, we use the proposed BMARD method to analyze local field potential (LFP) activity from the hippocampus of laboratory rats across different conditions in a non-spatial sequence memory experiment to identify the most interesting frequency bands and examine the link between specific patterns of activity and trial-specific cognitive demands.