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 frequency bands, defined a priori, 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 are not uniform across different cognitive demands. Thus, these bands should not be arbitrarily set in any analysis. To overcome this limitation, the Bayesian mixture auto-regressive decomposition (BMARD) method is proposed, as a data-driven approach that identifies (i) the number of prominent spectral peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks). Using the BMARD method, the standardized SDF is represented as 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. A Metropolis-Hastings within the Gibbs algorithm is developed for sampling the posterior distribution of the mixture parameters. Simulations demonstrate the robust performance of the proposed method. Finally, the BMARD method is applied 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 prominent frequency bands and examine the link between specific patterns of brain oscillatory activity and trial-specific cognitive demands.