  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.
