BRAIN WAVES ANALYSIS VIA A NON-PARAMETRIC BAYESIAN MIXTURE OF AUTOREGRESSIVE KERNELS BY GUILLERMO GRANADOS-GARCIA 1 ,MARK FIECAS 2,* BABAK SHAHBABA 3 NORBERT FORTIN 3 AND HERNANDO OMBAO 1 1 King Abdullah University of Science and Technology, guillermo.granadosgarcia@kaust.edu.sa; hernando.ombao@kaust.edu.sa 2 University of Minnesota, * mfiecas@umn.edu 3 University of California Irvine, babaks@uci.edu; norbert.fortin@uci.edu 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 SDF 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. We present a Metropolis-Hastings within Gibbs algorithm to sample from the posterior distribution of the mixture pa- rameters. Simulation studies demonstrate the robustness and performance of the BMARD method. Finally, we use the proposed BMARD method to ana- lyze 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. 1. Introduction. Considerable research indicates that the hippocampus — a brain re- gion highly conserved across mammals — plays a key role in our ability to remember the order in which daily life events occur (Eichenbaum, 2014). To identify the neuronal mech- anism underlying this capacity, we have conducted an experiment in which neural activities are recorded in the hippocampus of rats as they perform a complex nonspatial sequence mem- ory task. Visualization of the LFP activity in Figure 1 revealed a highly dynamic pattern of hippocampal oscillations during task performance detailed on Section 4, reflecting the dis- tinct cognitive demands at different moments in time. Notably, the specific frequencies and bandwidth of the observed oscillations did not map well with standard predefined frequency bands (delta, theta, alpha, beta and gamma bands). Our goal in this paper is to develop a statistical method to quantify the spectral properties of the LFPs, in particular identify the frequency peaks and bandwidth, and link them with specific types of information processing. Keywords and phrases: Spectral Density estimation, Bayesian nonparametrics, local field potentials, Dirichlet Process, Markov Chain Monte Carlo. 1 arXiv:2102.11971v2 [stat.ME] 8 Mar 2021